chore(tests): mass-update for pp.binder_types false
This commit is contained in:
Sebastian Ullrich
Leonardo de Moura
parent
f2200fab65
commit
273753f3fc
96 changed files with 297 additions and 328 deletions
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@ -12,5 +12,5 @@ P : group P₀
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⊢ ?M_1
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438.lean:10:2: error: failed to add declaration 'lambda_morphism.mk' to environment, type has metavariables
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remark: set 'formatter.hide_full_terms' to false to see the complete term
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Π {P₀ : Type} {P : …},
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Π {P₀} {P},
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?M_2 = ?M_3 → …
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@ -1 +1 @@
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is_contr.mk : Π (center : ?A), (Π (a : ?A), center = a) → is_contr ?A
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is_contr.mk : Π center, (Π a, center = a) → is_contr ?A
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@ -3,10 +3,10 @@ A : Type,
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B : Type,
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f : A → B,
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g : B → A,
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ε : Π (b : B), f (g b) = b,
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ε : Π b, f (g b) = b,
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b b' : B
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⊢ (ε b)⁻¹ ⬝ ε b = refl b
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487.hlean:19:0: error: failed to add declaration 'foo' to environment, value has metavariables
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remark: set 'formatter.hide_full_terms' to false to see the complete term
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λ (A : Type) (B : Type) (f : …) (g : …) (ε : …) (b b' : B),
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λ A B f g ε b b',
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is_retraction.mk … ?M_1
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@ -32,5 +32,5 @@ rinv : func ∘ finv = id
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⊢ inv (mk func finv linv rinv) ∘b mk func finv linv rinv = id
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550.lean:43:2: error: failed to add declaration 'bijection.inv.linv' to environment, value has metavariables
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remark: set 'formatter.hide_full_terms' to false to see the complete term
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λ (A : Type) (f : …),
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λ A f,
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bijection.rec_on f ?M_1
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@ -1,11 +1,11 @@
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571.lean:6:2: error:invalid 'cases' tactic, 'Exists' can only eliminate to Prop
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proof state:
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P : ℕ → Prop,
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H : ∃ (n : ℕ), P n
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H : ∃ n, P n
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⊢ ℕ
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571.lean:7:0: error: don't know how to synthesize placeholder
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P : ℕ → Prop,
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H : ∃ (n : ℕ), P n
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H : ∃ n, P n
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⊢ ℕ
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571.lean:7:0: error: failed to add declaration 'example' to environment, value has metavariables
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remark: set 'formatter.hide_full_terms' to false to see the complete term
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@ -10,5 +10,5 @@ P : f a⁻¹ * f a = 1
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⊢ f a⁻¹ = (f a)⁻¹
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583.lean:27:8: error: failed to add declaration 'group_hom.hom_map_inv' to environment, value has metavariables
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remark: set 'formatter.hide_full_terms' to false to see the complete term
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λ (A : Type) (B : Type) (s1 : …) (s2 : …) (f : …) (Hom : …) (a : A),
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λ A B s1 s2 f Hom a,
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?M_1 …
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@ -1,5 +1,5 @@
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foo : Π (A : Type) [H : inhabited A], A → A
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foo' : Π {A : Type} [H : inhabited A] {x : A}, A
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foo : Π A [H], A → A
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foo' : Π {A} [H] {x}, A
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foo ℕ 10 : ℕ
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definition test : ∀ {A : Type} [H : inhabited A], @foo' ℕ nat.is_inhabited (@has_add.add ℕ nat_has_add 5 5) = 10 :=
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λ (A : Type) (H : inhabited A), @rfl ℕ (@foo' ℕ nat.is_inhabited (@has_add.add ℕ nat_has_add 5 5))
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λ A H, @rfl ℕ (@foo' ℕ nat.is_inhabited (@has_add.add ℕ nat_has_add 5 5))
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@ -1,4 +1,4 @@
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tst₁ : Π (A : Type), A → A
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tst₂ : Π {A : Type}, A → A
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symm₂ : ∀ {A : Type} (a b : A), a = b → b = a
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tst₃ : Π (A : Type), A → A
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tst₁ : Π A, A → A
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tst₂ : Π {A}, A → A
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symm₂ : ∀ {A} a b, a = b → b = a
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tst₃ : Π A, A → A
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@ -1,5 +1,5 @@
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tst₁ : Π (A : Type), A → A
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tst₂ : Π {A : Type}, A → A
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symm₂ : ∀ {A : Type} (a b : A), a = b → b = a
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tst₃ : Π (A : Type), A → A
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foo : ∀ {A : Type} {a b : A}, a = b → (∀ (c : A), c = b → c = a)
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tst₁ : Π A, A → A
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tst₂ : Π {A}, A → A
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symm₂ : ∀ {A} a b, a = b → b = a
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tst₃ : Π A, A → A
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foo : ∀ {A} {a b}, a = b → (∀ c, c = b → c = a)
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@ -2,7 +2,7 @@
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A B : Type₁,
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s : setoid A,
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f : A → B,
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c : ∀ (a₁ a₂ : A), a₁ ≈ a₂ → f a₁ = f a₂,
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c : ∀ a₁ a₂, a₁ ≈ a₂ → f a₁ = f a₂,
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a : A,
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g h : B → B,
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gh : g = h
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@ -1,11 +1,11 @@
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definition id [reducible] [unfold_full] : Π {A : Type}, A → A :=
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λ (A : Type) (a : A), a
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λ A a, a
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definition category.id [reducible] [unfold 1] : Π {ob : Type} [C : precategory ob] {a : ob}, hom a a :=
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ID
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-----------
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definition id [reducible] [unfold_full] : Π {A : Type}, A → A
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λ (A : Type) (a : A), a
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λ A a, a
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definition category.id [reducible] [unfold 1] : Π {ob : Type} [C : precategory ob] {a : ob}, hom a a
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ID
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@ -3,8 +3,8 @@ x : S¹
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⊢ bool
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626b.hlean:4:50: error: don't know how to synthesize placeholder
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x : S¹
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⊢ eq.pathover (λ (a : S¹), bool) ?M_1 loop ?M_1
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⊢ eq.pathover (λ a, bool) ?M_1 loop ?M_1
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626b.hlean:4:32: error: failed to add declaration 'f' to environment, value has metavariables
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remark: set 'formatter.hide_full_terms' to false to see the complete term
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λ (x : S¹),
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λ x,
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circle.rec_on x ?M_1 ?M_2
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@ -1,5 +1,5 @@
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definition pnat.pnat : Type₁ :=
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{n : ℕ | n > 0}
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{n | n > 0}
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inductive prod : Type → Type → Type
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constructors:
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prod.mk : Π {A : Type} {B : Type}, A → B → A × B
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prod.mk : Π {A} {B}, A → B → A × B
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@ -3,8 +3,8 @@ _root_.A : Type₁ → Type₁
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A : Type.{l} → Type.{l}
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_root_.A.{1} : Type₁ → Type₁
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P : B → B
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_root_.P : Π {n : ℕ}, ℕ → ℕ
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_root_.P : Π {n}, ℕ → ℕ
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P : B → B
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_root_.P.{1} : ?B → ?B
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@P 2 : B → B
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@_root_.P.{1} ℕ : Π {n : ℕ}, ℕ → ℕ
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@_root_.P.{1} ℕ : Π {n}, ℕ → ℕ
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@ -2,9 +2,7 @@
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P : quotient S → Type,
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c c' : C,
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a : A
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⊢ pathover P (quotient.rec (λ (b : A), sorry) (λ (b b' : A) (H : R b b'), sorry) (f a unit.star))
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(eq_of_rel S (S.Rmk a unit.star))
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sorry
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⊢ pathover P (quotient.rec (λ b, sorry) (λ b b' H, sorry) (f a unit.star)) (eq_of_rel S (S.Rmk a unit.star)) sorry
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640.hlean:25:22: proof state
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P : quotient S → Type,
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c c' : C,
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@ -1 +1 @@
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eq : Π {A : Type}, A → A → Prop
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eq : Π {A}, A → A → Prop
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@ -1,4 +1,4 @@
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f (coe a) : B
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g (λ (x : C), coe (h x)) : B
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filter (λ (x : bool), bool_to_Prop (negb x)) [tt, ff, tt, ff] : list bool
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g (λ x, coe (h x)) : B
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filter (λ x, bool_to_Prop (negb x)) [tt, ff, tt, ff] : list bool
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[ff, ff]
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@ -1,6 +1,6 @@
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R : Π {b c : bool}, Prop
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R : Π {b c}, Prop
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R2 : bool → bool → Prop
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R3 : bool → bool → Prop
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R4 : bool → (Π {c : bool}, Prop)
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R5 : Π {b c : bool}, Prop
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R6 : Π {b : bool}, bool → Prop
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R4 : bool → (Π {c}, Prop)
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R5 : Π {b c}, Prop
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R6 : Π {b}, bool → Prop
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@ -6,7 +6,7 @@ but is expected to have type
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Prop
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the assignment was attempted when processing
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application type constraint
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(λ {T : Prop} (t : T), t) bool.tt
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(λ {T} t, t) bool.tt
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term
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bool.tt
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has type
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@ -1,2 +1,2 @@
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protected definition nat.add : ℕ → ℕ → ℕ :=
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λ (a : ℕ), nat.rec a (λ (b₁ : ℕ), nat.succ)
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λ a, nat.rec a (λ b₁, nat.succ)
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@ -12,7 +12,7 @@ q : u₂ =[p] v₂
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690.hlean:12:0: error: don't know how to synthesize placeholder
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A : Type,
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B : A → Type,
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u v : Σ (a : A), B a,
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u v : Σ a, B a,
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p : u.1 = v.1,
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q : u.2 =[p] v.2
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⊢ ⟨(sigma_eq p q)..1, (sigma_eq p q)..2⟩ = ⟨p, q⟩
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@ -11,13 +11,13 @@ p : P 0 (succ a)
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P Q : ℕ → ℕ → Prop,
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a : ℕ,
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v_0 : ∀ (m : ℕ), P a m → Q a m,
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v_0 : ∀ m, P a m → Q a m,
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p : P (succ a) 0
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⊢ Q (succ a) 0
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P Q : ℕ → ℕ → Prop,
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a : ℕ,
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v_0 : ∀ (m : ℕ), P a m → Q a m,
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v_0 : ∀ m, P a m → Q a m,
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a_1 : ℕ,
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v_0_1 : P (succ a) a_1 → Q (succ a) a_1,
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p : P (succ a) (succ a_1)
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@ -1,2 +1,2 @@
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definition foo : empty → empty :=
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empty.rec (λ (e : empty), empty)
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empty.rec (λ e, empty)
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@ -1,6 +1,6 @@
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definition tst : ℕ
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(λ (a : Type₁), 2 + 3) ℕ
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(λ a, 2 + 3) ℕ
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definition tst : ℕ
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foo ℕ
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definition tst1 : ℕ
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(λ (A : Type₁) (a : A), a) ℕ 10
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(λ A a, a) ℕ 10
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@ -1,4 +1,3 @@
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acc.rec :
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Π {A : Type} {R : A → A → Prop} {C : A → Type},
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(Π (x : A), (∀ (y : A), R y x → acc A R y) → (Π (y : A), R y x → C y) → C x) →
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(Π {a : A}, acc A R a → C a)
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Π {A} {R} {C},
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(Π x, (∀ y, R y x → acc A R y) → (Π y, R y x → C y) → C x) → (Π {a}, acc A R a → C a)
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@ -1,12 +1,3 @@
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F x₁
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(λ (y : A) (a : R y x₁),
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acc.rec (λ (x₂ : A) (ac : ∀ (y : A), R y x₂ → acc R y) (iH : Π (y : A), R y x₂ → C y), F x₂ iH)
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(ac y a))
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acc.rec (λ (x₂ : A) (ac : ∀ (y : A), R y x₂ → acc R y) (iH : Π (y : A), R y x₂ → C y), F x₂ iH)
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(acc.intro x₁ ac) :
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C x₁
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F x₁
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(λ (y : A) (a : R y x₁),
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acc.rec (λ (x₂ : A) (ac : ∀ (y : A), R y x₂ → acc R y) (iH : Π (y : A), R y x₂ → C y), F x₂ iH)
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(ac y a)) :
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C x₁
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F x₁ (λ y a, acc.rec (λ x₂ ac iH, F x₂ iH) (ac y a))
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acc.rec (λ x₂ ac iH, F x₂ iH) (acc.intro x₁ ac) : C x₁
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F x₁ (λ y a, acc.rec (λ x₂ ac iH, F x₂ iH) (ac y a)) : C x₁
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@ -1,8 +1,8 @@
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definition f : ℕ → ℕ :=
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λ (a : ℕ), a + 1
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λ a, a + 1
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definition f [reducible] : ℕ → ℕ :=
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λ (a : ℕ), a + 1
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λ a, a + 1
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definition f : ℕ → ℕ :=
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λ (a : ℕ), a + 1
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λ a, a + 1
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definition f [reducible] : ℕ → ℕ :=
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λ (a : ℕ), a + 1
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λ a, a + 1
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@ -1,35 +1,35 @@
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sec 3.
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definition foo.bah.bla.f [reducible] : ℕ → ℕ :=
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λ (a : ℕ), a + 1
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λ a, a + 1
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definition foo.bah.bla.g [reducible] : ℕ → ℕ :=
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λ (a : ℕ), a + a
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λ a, a + a
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sec 2.
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definition foo.bah.bla.f [reducible] : ℕ → ℕ :=
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λ (a : ℕ), a + 1
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λ a, a + 1
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definition foo.bah.bla.g [reducible] : ℕ → ℕ :=
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λ (a : ℕ), a + a
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λ a, a + a
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sec 1.
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definition foo.bah.bla.f [reducible] : ℕ → ℕ :=
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λ (a : ℕ), a + 1
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λ a, a + 1
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definition foo.bah.bla.g [reducible] : ℕ → ℕ :=
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λ (a : ℕ), a + a
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λ a, a + a
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foo.bah.bla.
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definition foo.bah.bla.f [reducible] : ℕ → ℕ :=
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λ (a : ℕ), a + 1
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λ a, a + 1
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definition foo.bah.bla.g [reducible] : ℕ → ℕ :=
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λ (a : ℕ), a + a
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λ a, a + a
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foo.bah.
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definition foo.bah.bla.f [reducible] : ℕ → ℕ :=
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λ (a : ℕ), a + 1
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λ a, a + 1
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definition foo.bah.bla.g [reducible] : ℕ → ℕ :=
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λ (a : ℕ), a + a
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λ a, a + a
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foo.
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definition foo.bah.bla.f : ℕ → ℕ :=
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λ (a : ℕ), a + 1
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λ a, a + 1
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definition foo.bah.bla.g [reducible] : ℕ → ℕ :=
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λ (a : ℕ), a + a
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λ a, a + a
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root.
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definition foo.bah.bla.f : ℕ → ℕ :=
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λ (a : ℕ), a + 1
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λ a, a + 1
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definition foo.bah.bla.g [reducible] : ℕ → ℕ :=
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λ (a : ℕ), a + a
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λ a, a + a
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@ -1,8 +1,8 @@
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definition bla.f : ℕ → ℕ :=
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λ (a : ℕ), a + 1
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λ a, a + 1
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definition bla.f [reducible] : ℕ → ℕ :=
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λ (a : ℕ), a + 1
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λ a, a + 1
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definition bla.f : ℕ → ℕ :=
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λ (a : ℕ), a + 1
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λ a, a + 1
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definition bla.f [reducible] : ℕ → ℕ :=
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λ (a : ℕ), a + 1
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λ a, a + 1
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@ -1,8 +1,8 @@
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definition foo : ∀ {A : Type} [_inst_1 : group A] (a b : A), a * b = b * a :=
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λ (A : Type) (_inst_1 : group A) (a b : A), sorry
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λ A _inst_1 a b, sorry
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definition bla : ∀ {B : Type} [_inst_2 : group B] (b : B), b * 1 = b :=
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λ (B : Type) (_inst_2 : group B) (b : B), sorry
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λ B _inst_2 b, sorry
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definition foo2 : ∀ {A : Type} [_inst_1 : group A] (a b : A), a * b = b * a :=
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λ (A : Type) (_inst_1 : group A) (a b : A), sorry
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λ A _inst_1 a b, sorry
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definition bla2 : ∀ {B : Type} [_inst_2 : group B] (b : B), b * 1 = b :=
|
||||
λ (B : Type) (_inst_2 : group B) (b : B), sorry
|
||||
λ B _inst_2 b, sorry
|
||||
|
|
|
|||
|
|
@ -1,15 +1,15 @@
|
|||
{x : ℕ ∈ S | x > 0} : set ℕ
|
||||
{x : ℕ ∈ s | x > 0} : finset ℕ
|
||||
{x ∈ S | x > 0} : set ℕ
|
||||
{x ∈ s | x > 0} : finset ℕ
|
||||
@set.sep.{1} nat
|
||||
(λ (x : nat),
|
||||
(λ x,
|
||||
@gt.{1} nat nat._trans_of_decidable_linear_ordered_semiring_13 x
|
||||
(@zero.{1} nat nat._trans_of_decidable_linear_ordered_semiring_6))
|
||||
S :
|
||||
set.{1} nat
|
||||
@finset.sep.{1} nat (λ (a b : nat), nat.has_decidable_eq a b)
|
||||
(λ (x : nat),
|
||||
@finset.sep.{1} nat (λ a b, nat.has_decidable_eq a b)
|
||||
(λ x,
|
||||
@gt.{1} nat nat._trans_of_decidable_linear_ordered_semiring_13 x
|
||||
(@zero.{1} nat nat._trans_of_decidable_linear_ordered_semiring_6))
|
||||
(λ (a : nat), nat.decidable_lt (@zero.{1} nat nat._trans_of_decidable_linear_ordered_semiring_6) a)
|
||||
(λ a, nat.decidable_lt (@zero.{1} nat nat._trans_of_decidable_linear_ordered_semiring_6) a)
|
||||
s :
|
||||
finset.{1} nat
|
||||
|
|
|
|||
|
|
@ -1,4 +1,4 @@
|
|||
definition lemma1 : ∀ (a : ℕ), r a → s a → p a :=
|
||||
λ (a : ℕ) (H.1 : r a) (H.2 : s a), rq₁ a H.1
|
||||
λ a H.1 H.2, rq₁ a H.1
|
||||
definition lemma2 : ∀ (a : ℕ), r a → s a → p a :=
|
||||
λ (a : ℕ) (H.1 : r a), rq₂ a
|
||||
λ a H.1, rq₂ a
|
||||
|
|
|
|||
|
|
@ -2,7 +2,7 @@ blast_cc_not_provable.lean:5:0: error: blast tactic failed
|
|||
strategy 'cc' failed, no proof found, final state:
|
||||
C : ℕ → Type,
|
||||
n m : ℕ,
|
||||
f : Π (n : ℕ), C n → C n,
|
||||
f : Π n, C n → C n,
|
||||
c : C n,
|
||||
d : C m,
|
||||
H.6 : f n == f m,
|
||||
|
|
@ -11,14 +11,14 @@ H.7 : c == d
|
|||
-------
|
||||
proof state:
|
||||
C : ℕ → Type,
|
||||
f : Π (n : ℕ), C n → C n,
|
||||
f : Π n, C n → C n,
|
||||
n m : ℕ,
|
||||
c : C n,
|
||||
d : C m
|
||||
⊢ f n == f m → c == d → f n c == f m d
|
||||
blast_cc_not_provable.lean:5:0: error: don't know how to synthesize placeholder
|
||||
C : ℕ → Type,
|
||||
f : Π (n : ℕ), C n → C n,
|
||||
f : Π n, C n → C n,
|
||||
n m : ℕ,
|
||||
c : C n,
|
||||
d : C m
|
||||
|
|
|
|||
|
|
@ -1,19 +1,19 @@
|
|||
bug1.lean:9:7: error: type mismatch at definition 'and_intro1', has type
|
||||
∀ (p q : bool),
|
||||
p → q → (∀ (c : bool), (p → q → c) → c)
|
||||
∀ p q,
|
||||
p → q → (∀ c, (p → q → c) → c)
|
||||
but is expected to have type
|
||||
∀ (p q : bool),
|
||||
∀ p q,
|
||||
p → q → a
|
||||
bug1.lean:13:7: error: type mismatch at definition 'and_intro2', has type
|
||||
∀ (p q : bool),
|
||||
p → q → (∀ (c : bool), (p → q → c) → c)
|
||||
∀ p q,
|
||||
p → q → (∀ c, (p → q → c) → c)
|
||||
but is expected to have type
|
||||
∀ (p q : bool),
|
||||
∀ p q,
|
||||
p → q → p ∧ p
|
||||
bug1.lean:17:7: error: type mismatch at definition 'and_intro3', has type
|
||||
∀ (p q : bool),
|
||||
p → q → (∀ (c : bool), (p → q → c) → c)
|
||||
∀ p q,
|
||||
p → q → (∀ c, (p → q → c) → c)
|
||||
but is expected to have type
|
||||
∀ (p q : bool),
|
||||
∀ p q,
|
||||
p → q → q ∧ p
|
||||
and_intro4 : ∀ (p q : bool), p → q → p ∧ q
|
||||
and_intro4 : ∀ p q, p → q → p ∧ q
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
calc_assistant.lean:7:14: error: type mismatch at term
|
||||
H₁
|
||||
has type
|
||||
∀ (x : num),
|
||||
∀ x,
|
||||
b = x
|
||||
but is expected to have type
|
||||
a = b
|
||||
|
|
|
|||
|
|
@ -5,8 +5,7 @@ auxiliary goal at time of failure
|
|||
b r t l : z = z,
|
||||
s : square t b l r,
|
||||
e_3 : z = z
|
||||
⊢ Π (e_4 : eq.rec t (refl z) = idp) (e_5 : eq.rec (eq.rec b (refl z)) e_3 = idp) (e_6 : eq.rec l (refl z) = idp)
|
||||
(e_7 : eq.rec (eq.rec r (refl z)) e_3 = idp),
|
||||
⊢ Π e_4 e_5 e_6 e_7,
|
||||
eq.rec (eq.rec (eq.rec (eq.rec (eq.rec (eq.rec (eq.rec s (refl z)) (refl z)) e_3) e_4) e_5) e_6)
|
||||
e_7 = square.ids →
|
||||
unit
|
||||
|
|
|
|||
|
|
@ -1,4 +1,4 @@
|
|||
and.intro : ?a → ?b → ?a ∧ ?b
|
||||
or.elim : ?a ∨ ?b → (?a → ?c) → (?b → ?c) → ?c
|
||||
eq : ?A → ?A → Prop
|
||||
eq.rec : ?C ?a → (Π {a : ?A}, ?a = a → ?C a)
|
||||
eq.rec : ?C ?a → (Π {a}, ?a = a → ?C a)
|
||||
|
|
|
|||
|
|
@ -1,3 +1,3 @@
|
|||
pr : Π {A : Type}, A → A → A
|
||||
pr : Π {A}, A → A → A
|
||||
pr a b : N
|
||||
pr a b : N
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
f (int.of_nat a) : int
|
||||
λ (x : bv a), @g a x : bv a → bv a
|
||||
λ x, @g a x : bv a → bv a
|
||||
coe2.lean:19:6: error: type mismatch at application
|
||||
f a
|
||||
term
|
||||
|
|
|
|||
|
|
@ -1,19 +1,15 @@
|
|||
theorem perm.perm_erase_dup_of_perm [congr] : ∀ {A : Type} [H : decidable_eq A] {l₁ l₂ : list A}, l₁ ~ l₂ → erase_dup l₁ ~ erase_dup l₂ :=
|
||||
λ (A : Type) (H : decidable_eq A) (l₁ l₂ : list A) (p : l₁ ~ l₂),
|
||||
λ A H l₁ l₂ p,
|
||||
perm_induction_on p nil
|
||||
(λ (x : A) (t₁ t₂ : list A) (p : t₁ ~ t₂) (r : erase_dup t₁ ~ erase_dup t₂),
|
||||
decidable.by_cases (λ (xint₁ : x ∈ t₁), have xint₂ : x ∈ t₂, from mem_of_mem_erase_dup …, … …)
|
||||
(λ (nxint₁ : x ∉ t₁),
|
||||
have nxint₂ : x ∉ t₂, from λ (xint₂ : x ∈ t₂), … nxint₁,
|
||||
eq.rec … (eq.symm …)))
|
||||
(λ (y x : A) (t₁ t₂ : list A) (p : t₁ ~ t₂) (r : erase_dup t₁ ~ erase_dup t₂),
|
||||
(λ x t₁ t₂ p r,
|
||||
decidable.by_cases (λ xint₁, have xint₂ : x ∈ t₂, from mem_of_mem_erase_dup …, … …)
|
||||
(λ nxint₁, have nxint₂ : x ∉ t₂, from λ xint₂, … nxint₁, eq.rec … (eq.symm …)))
|
||||
(λ y x t₁ t₂ p r,
|
||||
decidable.by_cases
|
||||
(λ (xinyt₁ : x ∈ y :: t₁),
|
||||
decidable.by_cases (λ (yint₁ : …), …)
|
||||
(λ (nyint₁ : y ∉ t₁), have nyint₂ : …, from …, …))
|
||||
(λ (nxinyt₁ : x ∉ y :: t₁),
|
||||
(λ xinyt₁, decidable.by_cases (λ yint₁, …) (λ nyint₁, have nyint₂ : …, from …, …))
|
||||
(λ nxinyt₁,
|
||||
have xney : x ≠ y, from ne_of_not_mem_cons nxinyt₁,
|
||||
have nxint₁ : x ∉ t₁, from not_mem_of_not_mem_cons nxinyt₁,
|
||||
have nxint₂ : x ∉ t₂, from λ (xint₂ : …), …,
|
||||
have nxint₂ : x ∉ t₂, from λ xint₂, …,
|
||||
… …))
|
||||
(λ (t₁ t₂ t₃ : list A) (p₁ : t₁ ~ t₂) (p₂ : t₂ ~ t₃), trans)
|
||||
(λ t₁ t₂ t₃ p₁ p₂, trans)
|
||||
|
|
|
|||
|
|
@ -1,8 +1,8 @@
|
|||
λ (x y z w : A), q (q (q w))
|
||||
A → A → A → (∀ (w : A), q (q (q w)) = w)
|
||||
λ (x y z w : A), q (f (q (q x)) (q (q z)) (q w))
|
||||
∀ (x : A), A → (∀ (z w : A), q (f (q (q x)) (q (q z)) (q w)) = w)
|
||||
λ (x y z w : A), q (q (q w))
|
||||
A → A → A → (∀ (w : A), q (q (q w)) = w)
|
||||
λ (x y z w : A), w
|
||||
A → A → A → (∀ (w : A), w = w)
|
||||
λ x y z w, q (q (q w))
|
||||
A → A → A → (∀ w, q (q (q w)) = w)
|
||||
λ x y z w, q (f (q (q x)) (q (q z)) (q w))
|
||||
∀ x, A → (∀ z w, q (f (q (q x)) (q (q z)) (q w)) = w)
|
||||
λ x y z w, q (q (q w))
|
||||
A → A → A → (∀ w, q (q (q w)) = w)
|
||||
λ x y z w, w
|
||||
A → A → A → (∀ w, w = w)
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
eq_class_error.lean:15:10: error: don't know how to synthesize placeholder
|
||||
decidable_eq_foo : Π (f₁ f₂ : foo), decidable (f₁ = f₂)
|
||||
decidable_eq_foo : Π f₁ f₂, decidable (f₁ = f₂)
|
||||
⊢ decidable (b = b)
|
||||
eq_class_error.lean:9:11: error: failed to synthesize placeholder
|
||||
|
||||
⊢ Π (f₁ f₂ : foo),
|
||||
⊢ Π f₁ f₂,
|
||||
decidable (f₁ = f₂)
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
error_pos_bug.lean:9:0: error: type error in placeholder assigned to
|
||||
λ (a : Category) (b : Category) (c : Category),
|
||||
λ a b c,
|
||||
a
|
||||
placeholder has type
|
||||
Category
|
||||
|
|
|
|||
|
|
@ -5,4 +5,4 @@ errors.lean:22:12: error: unknown identifier 'b'
|
|||
tst3 : A → A → A
|
||||
foo.tst1 : ℕ → ℕ → ℕ
|
||||
foo.tst2 : ℕ → ℕ → ℕ
|
||||
foo.tst3 : Π (A : Type), A → A → A
|
||||
foo.tst3 : Π A, A → A → A
|
||||
|
|
|
|||
|
|
@ -1 +1 @@
|
|||
λ (A : Type) (x y : A) (H₁ : x = y) (H₂ : y = x), eq.rec H₁ H₂
|
||||
λ A x y H₁ H₂, eq.rec H₁ H₂
|
||||
|
|
|
|||
|
|
@ -1,4 +1,2 @@
|
|||
to_set_union :
|
||||
∀ {A : Type} [deceq : decidable_eq A] (s t : finset A),
|
||||
@eq (set A) (@ts A (@union A deceq s t)) (@set.union A (@ts A s) (@ts A t))
|
||||
to_set_empty : ∀ {A : Type}, @eq (set A) (@ts A (@empty A)) (@set.empty A)
|
||||
to_set_union : ∀ {A} [deceq] s t, @eq (set A) (@ts A (@union A deceq s t)) (@set.union A (@ts A s) (@ts A t))
|
||||
to_set_empty : ∀ {A}, @eq (set A) (@ts A (@empty A)) (@set.empty A)
|
||||
|
|
|
|||
|
|
@ -3,6 +3,6 @@ position 55:52
|
|||
A : Type,
|
||||
B : Type,
|
||||
f : one_step_tr A → B
|
||||
⊢ Π (x y : A),
|
||||
⊢ Π x y,
|
||||
f (tr x) = f (tr y)
|
||||
END_LEAN_INFORMATION
|
||||
|
|
|
|||
|
|
@ -2,9 +2,7 @@ LEAN_INFORMATION
|
|||
position 671:8
|
||||
A : Type,
|
||||
decA : decidable_eq A,
|
||||
ex_of_subcount_eq_ff :
|
||||
∀ {l₁ l₂ : list A},
|
||||
subcount l₁ l₂ = ff → (∃ (a : A), ¬list.count a l₁ ≤ list.count a l₂),
|
||||
ex_of_subcount_eq_ff : ∀ {l₁ l₂}, subcount l₁ l₂ = ff → (∃ a, ¬list.count a l₁ ≤ list.count a l₂),
|
||||
a : A,
|
||||
l₁ l₂ : list A,
|
||||
h : subcount (a :: l₁) l₂ = ff,
|
||||
|
|
|
|||
|
|
@ -2,15 +2,13 @@ LEAN_INFORMATION
|
|||
position 677:47
|
||||
A : Type,
|
||||
decA : decidable_eq A,
|
||||
ex_of_subcount_eq_ff :
|
||||
∀ {l₁ l₂ : list A},
|
||||
subcount l₁ l₂ = ff → (∃ (a : A), ¬list.count a l₁ ≤ list.count a l₂),
|
||||
ex_of_subcount_eq_ff : ∀ {l₁ l₂}, subcount l₁ l₂ = ff → (∃ a, ¬list.count a l₁ ≤ list.count a l₂),
|
||||
a : A,
|
||||
l₁ l₂ : list A,
|
||||
h : subcount (a :: l₁) l₂ = ff,
|
||||
i : list.count a (a :: l₁) ≤ list.count a l₂,
|
||||
this : subcount l₁ l₂ = ff,
|
||||
ih : ∃ (a : A), ¬list.count a l₁ ≤ list.count a l₂,
|
||||
ih : ∃ a, ¬list.count a l₁ ≤ list.count a l₂,
|
||||
hw : ¬list.count a l₁ ≤ list.count a l₂
|
||||
⊢ ¬list.count a (a :: l₁) ≤ list.count a l₂
|
||||
END_LEAN_INFORMATION
|
||||
|
|
|
|||
|
|
@ -13,23 +13,23 @@ A : Type,
|
|||
h : decidable_eq A,
|
||||
P : finset A → Prop,
|
||||
H1 : P (@empty A),
|
||||
H2 : ∀ ⦃s : finset A⦄ {a : A}, not (@mem A a s) → P s → P (@insert A h a s),
|
||||
H2 : ∀ ⦃s⦄ {a}, not (@mem A a s) → P s → P (@insert A h a s),
|
||||
s : finset A,
|
||||
u : nodup_list A,
|
||||
l : list A,
|
||||
a : A,
|
||||
l' : list A,
|
||||
IH :
|
||||
∀ (has_property : @nodup A l'),
|
||||
∀ has_property,
|
||||
P (@quot.mk (nodup_list A) (nodup_list_setoid A) (@subtype.tag (list A) (@nodup A) l' has_property)),
|
||||
nodup_al' : @nodup A (@cons A a l'),
|
||||
anl' : not (@list.mem A a l'),
|
||||
H3 : @eq (list A) (@list.insert A (λ (a b : A), h a b) a l') (@cons A a l'),
|
||||
H3 : @eq (list A) (@list.insert A (λ a b, h a b) a l') (@cons A a l'),
|
||||
nodup_l' : @nodup A l',
|
||||
P_l' : P (@quot.mk (nodup_list A) (nodup_list_setoid A) (@subtype.tag (list A) (@nodup A) l' nodup_l')),
|
||||
H4 :
|
||||
P
|
||||
(@insert A (λ (a b : A), h a b) a
|
||||
(@insert A (λ a b, h a b) a
|
||||
(@quot.mk (nodup_list A) (nodup_list_setoid A) (@subtype.tag (list A) (@nodup A) l' nodup_l')))
|
||||
⊢ P (@quot.mk (nodup_list A) (nodup_list_setoid A) (@subtype.tag (list A) (@nodup A) (@cons A a l') nodup_al'))
|
||||
finset_induction_bug.lean:30:45: error: don't know how to synthesize placeholder
|
||||
|
|
@ -37,34 +37,34 @@ A : Type,
|
|||
h : decidable_eq A,
|
||||
P : finset A → Prop,
|
||||
H1 : P (@empty A),
|
||||
H2 : ∀ ⦃s : finset A⦄ {a : A}, not (@mem A a s) → P s → P (@insert A h a s),
|
||||
H2 : ∀ ⦃s⦄ {a}, not (@mem A a s) → P s → P (@insert A h a s),
|
||||
s : finset A,
|
||||
u : nodup_list A,
|
||||
l : list A,
|
||||
a : A,
|
||||
l' : list A,
|
||||
IH :
|
||||
∀ (has_property : @nodup A l'),
|
||||
∀ has_property,
|
||||
P (@quot.mk (nodup_list A) (nodup_list_setoid A) (@subtype.tag (list A) (@nodup A) l' has_property)),
|
||||
nodup_al' : @nodup A (@cons A a l'),
|
||||
anl' : not (@list.mem A a l'),
|
||||
H3 : @eq (list A) (@list.insert A (λ (a b : A), h a b) a l') (@cons A a l'),
|
||||
H3 : @eq (list A) (@list.insert A (λ a b, h a b) a l') (@cons A a l'),
|
||||
nodup_l' : @nodup A l',
|
||||
P_l' : P (@quot.mk (nodup_list A) (nodup_list_setoid A) (@subtype.tag (list A) (@nodup A) l' nodup_l')),
|
||||
H4 :
|
||||
P
|
||||
(@insert A (λ (a b : A), h a b) a
|
||||
(@insert A (λ a b, h a b) a
|
||||
(@quot.mk (nodup_list A) (nodup_list_setoid A) (@subtype.tag (list A) (@nodup A) l' nodup_l')))
|
||||
⊢ P (@quot.mk (nodup_list A) (nodup_list_setoid A) (@subtype.tag (list A) (@nodup A) (@cons A a l') nodup_al'))
|
||||
finset_induction_bug.lean:16:5: error: failed to add declaration 'finset.induction₂' to environment, value has metavariables
|
||||
remark: set 'formatter.hide_full_terms' to false to see the complete term
|
||||
λ (A : Type) (h : …) (P : …) (H1 : …) (H2 : …) (s : …),
|
||||
λ A h P H1 H2 s,
|
||||
@quot.induction_on … … P s
|
||||
(λ (u : …),
|
||||
(λ u,
|
||||
@subtype.destruct … … … u
|
||||
(λ (l : …),
|
||||
(λ l,
|
||||
@list.induction_on A … l …
|
||||
(λ (a : A) (l' : …) (IH : …) (nodup_al' : …),
|
||||
(λ a l' IH nodup_al',
|
||||
have anl' : …, from …,
|
||||
have H3 : …, from …,
|
||||
have nodup_l' : …, from …,
|
||||
|
|
|
|||
|
|
@ -1,4 +1,4 @@
|
|||
gen_as.lean:7:2: proof state
|
||||
x y : ℕ
|
||||
⊢ ∀ (n : ℕ),
|
||||
⊢ ∀ n,
|
||||
n ≥ 0
|
||||
|
|
|
|||
|
|
@ -5,42 +5,42 @@
|
|||
-- BEGINFINDP
|
||||
bool.tt_bxor_tt|eq (bool.bxor bool.tt bool.tt) bool.ff
|
||||
bool.tt_bxor_ff|eq (bool.bxor bool.tt bool.ff) bool.tt
|
||||
bool.bor_tt|∀ (a : bool), eq (bool.bor a bool.tt) bool.tt
|
||||
bool.band_tt|∀ (a : bool), eq (bool.band a bool.tt) a
|
||||
bool.bor_tt|∀ a, eq (bool.bor a bool.tt) bool.tt
|
||||
bool.band_tt|∀ a, eq (bool.band a bool.tt) a
|
||||
bool.tt|bool
|
||||
bool.bxor_tt|∀ (a : bool), eq (bool.bxor a bool.tt) (bool.bnot a)
|
||||
bool.bxor_tt|∀ a, eq (bool.bxor a bool.tt) (bool.bnot a)
|
||||
bool.eq_tt_of_bnot_eq_ff|eq (bool.bnot ?a) bool.ff → eq ?a bool.tt
|
||||
bool.eq_ff_of_bnot_eq_tt|eq (bool.bnot ?a) bool.tt → eq ?a bool.ff
|
||||
bool.ff_bxor_tt|eq (bool.bxor bool.ff bool.tt) bool.tt
|
||||
bool.absurd_of_eq_ff_of_eq_tt|eq ?a bool.ff → eq ?a bool.tt → ?B
|
||||
bool.eq_tt_of_ne_ff|ne ?a bool.ff → eq ?a bool.tt
|
||||
tactic.with_attributes_tac|tactic.expr → tactic.identifier_list → tactic → tactic
|
||||
bool.tt_band|∀ (a : bool), eq (bool.band bool.tt a) a
|
||||
bool.cond_tt|∀ (t e : ?A), eq (bool.cond bool.tt t e) t
|
||||
bool.tt_band|∀ a, eq (bool.band bool.tt a) a
|
||||
bool.cond_tt|∀ t e, eq (bool.cond bool.tt t e) t
|
||||
bool.ff_ne_tt|eq bool.ff bool.tt → false
|
||||
bool.eq_ff_of_ne_tt|ne ?a bool.tt → eq ?a bool.ff
|
||||
bool.tt_bxor|∀ (a : bool), eq (bool.bxor bool.tt a) (bool.bnot a)
|
||||
bool.tt_bor|∀ (a : bool), eq (bool.bor bool.tt a) bool.tt
|
||||
bool.tt_bxor|∀ a, eq (bool.bxor bool.tt a) (bool.bnot a)
|
||||
bool.tt_bor|∀ a, eq (bool.bor bool.tt a) bool.tt
|
||||
-- ENDFINDP
|
||||
-- BEGINWAIT
|
||||
-- ENDWAIT
|
||||
-- BEGINFINDP
|
||||
tt|bool
|
||||
tt_bor|∀ (a : bool), eq (bor tt a) tt
|
||||
tt_band|∀ (a : bool), eq (band tt a) a
|
||||
tt_bxor|∀ (a : bool), eq (bxor tt a) (bnot a)
|
||||
tt_bor|∀ a, eq (bor tt a) tt
|
||||
tt_band|∀ a, eq (band tt a) a
|
||||
tt_bxor|∀ a, eq (bxor tt a) (bnot a)
|
||||
tt_bxor_tt|eq (bxor tt tt) ff
|
||||
tt_bxor_ff|eq (bxor tt ff) tt
|
||||
bor_tt|∀ (a : bool), eq (bor a tt) tt
|
||||
band_tt|∀ (a : bool), eq (band a tt) a
|
||||
bxor_tt|∀ (a : bool), eq (bxor a tt) (bnot a)
|
||||
bor_tt|∀ a, eq (bor a tt) tt
|
||||
band_tt|∀ a, eq (band a tt) a
|
||||
bxor_tt|∀ a, eq (bxor a tt) (bnot a)
|
||||
eq_tt_of_bnot_eq_ff|eq (bnot ?a) ff → eq ?a tt
|
||||
eq_ff_of_bnot_eq_tt|eq (bnot ?a) tt → eq ?a ff
|
||||
ff_bxor_tt|eq (bxor ff tt) tt
|
||||
absurd_of_eq_ff_of_eq_tt|eq ?a ff → eq ?a tt → ?B
|
||||
eq_tt_of_ne_ff|ne ?a ff → eq ?a tt
|
||||
tactic.with_attributes_tac|tactic.expr → tactic.identifier_list → tactic → tactic
|
||||
cond_tt|∀ (t e : ?A), eq (cond tt t e) t
|
||||
cond_tt|∀ t e, eq (cond tt t e) t
|
||||
ff_ne_tt|eq ff tt → false
|
||||
eq_ff_of_ne_tt|ne ?a tt → eq ?a ff
|
||||
-- ENDFINDP
|
||||
|
|
|
|||
|
|
@ -1,12 +1,12 @@
|
|||
-- BEGINWAIT
|
||||
-- ENDWAIT
|
||||
-- BEGINFINDP
|
||||
le.rec_on|le ?a ?a → (Π (a : nat), ?C a a) → ?C ?a ?a
|
||||
nat.rec_on|Π (n : nat), ?C 0 → (Π (a : nat), ?C a → ?C (succ a)) → ?C n
|
||||
bool.rec_on|Π (n : bool), ?C bool.ff → ?C bool.tt → ?C n
|
||||
le.rec_on|le ?a ?a → (Π a, ?C a a) → ?C ?a ?a
|
||||
nat.rec_on|Π n, ?C 0 → (Π a, ?C a → ?C (succ a)) → ?C n
|
||||
bool.rec_on|Π n, ?C bool.ff → ?C bool.tt → ?C n
|
||||
-- ENDFINDP
|
||||
-- BEGINFINDP
|
||||
nat.le.rec_on|nat.le ?a ?a → (Π (a : nat), ?C a a) → ?C ?a ?a
|
||||
nat.rec_on|Π (n : nat), ?C 0 → (Π (a : nat), ?C a → ?C (nat.succ a)) → ?C n
|
||||
bool.rec_on|Π (n : bool), ?C bool.ff → ?C bool.tt → ?C n
|
||||
nat.le.rec_on|nat.le ?a ?a → (Π a, ?C a a) → ?C ?a ?a
|
||||
nat.rec_on|Π n, ?C 0 → (Π a, ?C a → ?C (nat.succ a)) → ?C n
|
||||
bool.rec_on|Π n, ?C bool.ff → ?C bool.tt → ?C n
|
||||
-- ENDFINDP
|
||||
|
|
|
|||
|
|
@ -41,7 +41,7 @@ by
|
|||
rewrite
|
||||
-- ACK
|
||||
-- TYPE|7|42
|
||||
∀ (a_1 b_1 c_1 : ?A), (:a_1 + b_1 + c_1:) = (:a_1 + (b_1 + c_1):)
|
||||
∀ a_1 b_1 c_1, (:a_1 + b_1 + c_1:) = (:a_1 + (b_1 + c_1):)
|
||||
-- ACK
|
||||
-- IDENTIFIER|7|42
|
||||
add.assoc
|
||||
|
|
|
|||
|
|
@ -51,7 +51,7 @@ b₂
|
|||
c₂
|
||||
-- ACK
|
||||
-- TYPE|134|38
|
||||
Π (a : A), B a → Type
|
||||
Π a, B a → Type
|
||||
-- ACK
|
||||
-- IDENTIFIER|134|38
|
||||
C
|
||||
|
|
|
|||
|
|
@ -3,18 +3,18 @@
|
|||
-- BEGINWAIT
|
||||
-- ENDWAIT
|
||||
-- BEGINEVAL
|
||||
my_id : Π {A : Type}, A → A
|
||||
my_id : Π {A}, A → A
|
||||
-- ENDEVAL
|
||||
-- BEGINEVAL
|
||||
my_id2 : Π {A : Type}, A → A
|
||||
my_id2 : Π {A}, A → A
|
||||
-- ENDEVAL
|
||||
-- BEGINSAVE
|
||||
-- ENDSAVE
|
||||
-- BEGINWAIT
|
||||
-- ENDWAIT
|
||||
-- BEGINEVAL
|
||||
my_id : Π {A : Type}, A → A
|
||||
my_id : Π {A}, A → A
|
||||
-- ENDEVAL
|
||||
-- BEGINEVAL
|
||||
my_id2 : Π {A : Type}, A → A
|
||||
my_id2 : Π {A}, A → A
|
||||
-- ENDEVAL
|
||||
|
|
|
|||
|
|
@ -9,23 +9,23 @@ pos_num.is_inhabited|inhabited pos_num
|
|||
pos_num.is_one|pos_num → bool
|
||||
pos_num.inc|pos_num → pos_num
|
||||
pos_num.ibelow|pos_num → Prop
|
||||
pos_num.binduction_on|Π (n : pos_num), (Π (n : pos_num), pos_num.ibelow n → ?C n) → ?C n
|
||||
pos_num.induction_on|Π (n : pos_num), ?C pos_num.one → (Π (a : pos_num), ?C a → ?C (pos_num.bit1 a)) → (Π (a : pos_num), ?C a → ?C (pos_num.bit0 a)) → ?C n
|
||||
pos_num.binduction_on|Π n, (Π n, pos_num.ibelow n → ?C n) → ?C n
|
||||
pos_num.induction_on|Π n, ?C pos_num.one → (Π a, ?C a → ?C (pos_num.bit1 a)) → (Π a, ?C a → ?C (pos_num.bit0 a)) → ?C n
|
||||
pos_num.succ|pos_num → pos_num
|
||||
pos_num.bit1|pos_num → pos_num
|
||||
pos_num.rec|?C pos_num.one → (Π (a : pos_num), ?C a → ?C (pos_num.bit1 a)) → (Π (a : pos_num), ?C a → ?C (pos_num.bit0 a)) → (Π (n : pos_num), ?C n)
|
||||
pos_num.rec|?C pos_num.one → (Π a, ?C a → ?C (pos_num.bit1 a)) → (Π a, ?C a → ?C (pos_num.bit0 a)) → (Π n, ?C n)
|
||||
pos_num.one|pos_num
|
||||
pos_num.below|pos_num → Type
|
||||
pos_num.le|pos_num → pos_num → bool
|
||||
pos_num.cases_on|Π (n : pos_num), ?C pos_num.one → (Π (a : pos_num), ?C (pos_num.bit1 a)) → (Π (a : pos_num), ?C (pos_num.bit0 a)) → ?C n
|
||||
pos_num.cases_on|Π n, ?C pos_num.one → (Π a, ?C (pos_num.bit1 a)) → (Π a, ?C (pos_num.bit0 a)) → ?C n
|
||||
pos_num.pred|pos_num → pos_num
|
||||
pos_num.mul|pos_num → pos_num → pos_num
|
||||
pos_num.no_confusion_type|Type → pos_num → pos_num → Type
|
||||
pos_num.num_bits|pos_num → pos_num
|
||||
pos_num.no_confusion|eq ?v1 ?v2 → pos_num.no_confusion_type ?P ?v1 ?v2
|
||||
pos_num.lt|pos_num → pos_num → bool
|
||||
pos_num.rec_on|Π (n : pos_num), ?C pos_num.one → (Π (a : pos_num), ?C a → ?C (pos_num.bit1 a)) → (Π (a : pos_num), ?C a → ?C (pos_num.bit0 a)) → ?C n
|
||||
pos_num.brec_on|Π (n : pos_num), (Π (n : pos_num), pos_num.below n → ?C n) → ?C n
|
||||
pos_num.rec_on|Π n, ?C pos_num.one → (Π a, ?C a → ?C (pos_num.bit1 a)) → (Π a, ?C a → ?C (pos_num.bit0 a)) → ?C n
|
||||
pos_num.brec_on|Π n, (Π n, pos_num.below n → ?C n) → ?C n
|
||||
pos_num.add|pos_num → pos_num → pos_num
|
||||
pos_num_has_mul|has_mul pos_num
|
||||
pos_num|Type
|
||||
|
|
@ -43,22 +43,22 @@ pos_num.is_inhabited|inhabited pos_num
|
|||
pos_num.is_one|pos_num → bool
|
||||
pos_num.inc|pos_num → pos_num
|
||||
pos_num.ibelow|pos_num → Prop
|
||||
pos_num.binduction_on|Π (n : pos_num), (Π (n : pos_num), pos_num.ibelow n → ?C n) → ?C n
|
||||
pos_num.induction_on|Π (n : pos_num), ?C pos_num.one → (Π (a : pos_num), ?C a → ?C (pos_num.bit1 a)) → (Π (a : pos_num), ?C a → ?C (pos_num.bit0 a)) → ?C n
|
||||
pos_num.binduction_on|Π n, (Π n, pos_num.ibelow n → ?C n) → ?C n
|
||||
pos_num.induction_on|Π n, ?C pos_num.one → (Π a, ?C a → ?C (pos_num.bit1 a)) → (Π a, ?C a → ?C (pos_num.bit0 a)) → ?C n
|
||||
pos_num.succ|pos_num → pos_num
|
||||
pos_num.bit1|pos_num → pos_num
|
||||
pos_num.rec|?C pos_num.one → (Π (a : pos_num), ?C a → ?C (pos_num.bit1 a)) → (Π (a : pos_num), ?C a → ?C (pos_num.bit0 a)) → (Π (n : pos_num), ?C n)
|
||||
pos_num.rec|?C pos_num.one → (Π a, ?C a → ?C (pos_num.bit1 a)) → (Π a, ?C a → ?C (pos_num.bit0 a)) → (Π n, ?C n)
|
||||
pos_num.one|pos_num
|
||||
pos_num.below|pos_num → Type
|
||||
pos_num.le|pos_num → pos_num → bool
|
||||
pos_num.cases_on|Π (n : pos_num), ?C pos_num.one → (Π (a : pos_num), ?C (pos_num.bit1 a)) → (Π (a : pos_num), ?C (pos_num.bit0 a)) → ?C n
|
||||
pos_num.cases_on|Π n, ?C pos_num.one → (Π a, ?C (pos_num.bit1 a)) → (Π a, ?C (pos_num.bit0 a)) → ?C n
|
||||
pos_num.pred|pos_num → pos_num
|
||||
pos_num.mul|pos_num → pos_num → pos_num
|
||||
pos_num.no_confusion_type|Type → pos_num → pos_num → Type
|
||||
pos_num.no_confusion|eq ?v1 ?v2 → pos_num.no_confusion_type ?P ?v1 ?v2
|
||||
pos_num.lt|pos_num → pos_num → bool
|
||||
pos_num.rec_on|Π (n : pos_num), ?C pos_num.one → (Π (a : pos_num), ?C a → ?C (pos_num.bit1 a)) → (Π (a : pos_num), ?C a → ?C (pos_num.bit0 a)) → ?C n
|
||||
pos_num.brec_on|Π (n : pos_num), (Π (n : pos_num), pos_num.below n → ?C n) → ?C n
|
||||
pos_num.rec_on|Π n, ?C pos_num.one → (Π a, ?C a → ?C (pos_num.bit1 a)) → (Π a, ?C a → ?C (pos_num.bit0 a)) → ?C n
|
||||
pos_num.brec_on|Π n, (Π n, pos_num.below n → ?C n) → ?C n
|
||||
pos_num.add|pos_num → pos_num → pos_num
|
||||
pos_num_has_mul|has_mul pos_num
|
||||
pos_num|Type
|
||||
|
|
@ -72,22 +72,22 @@ pos_num.is_inhabited|inhabited pos_num
|
|||
pos_num.is_one|pos_num → bool
|
||||
pos_num.inc|pos_num → pos_num
|
||||
pos_num.ibelow|pos_num → Prop
|
||||
pos_num.binduction_on|Π (n : pos_num), (Π (n : pos_num), pos_num.ibelow n → ?C n) → ?C n
|
||||
pos_num.induction_on|Π (n : pos_num), ?C pos_num.one → (Π (a : pos_num), ?C a → ?C (pos_num.bit1 a)) → (Π (a : pos_num), ?C a → ?C (pos_num.bit0 a)) → ?C n
|
||||
pos_num.binduction_on|Π n, (Π n, pos_num.ibelow n → ?C n) → ?C n
|
||||
pos_num.induction_on|Π n, ?C pos_num.one → (Π a, ?C a → ?C (pos_num.bit1 a)) → (Π a, ?C a → ?C (pos_num.bit0 a)) → ?C n
|
||||
pos_num.succ|pos_num → pos_num
|
||||
pos_num.bit1|pos_num → pos_num
|
||||
pos_num.rec|?C pos_num.one → (Π (a : pos_num), ?C a → ?C (pos_num.bit1 a)) → (Π (a : pos_num), ?C a → ?C (pos_num.bit0 a)) → (Π (n : pos_num), ?C n)
|
||||
pos_num.rec|?C pos_num.one → (Π a, ?C a → ?C (pos_num.bit1 a)) → (Π a, ?C a → ?C (pos_num.bit0 a)) → (Π n, ?C n)
|
||||
pos_num.one|pos_num
|
||||
pos_num.below|pos_num → Type
|
||||
pos_num.le|pos_num → pos_num → bool
|
||||
pos_num.cases_on|Π (n : pos_num), ?C pos_num.one → (Π (a : pos_num), ?C (pos_num.bit1 a)) → (Π (a : pos_num), ?C (pos_num.bit0 a)) → ?C n
|
||||
pos_num.cases_on|Π n, ?C pos_num.one → (Π a, ?C (pos_num.bit1 a)) → (Π a, ?C (pos_num.bit0 a)) → ?C n
|
||||
pos_num.pred|pos_num → pos_num
|
||||
pos_num.mul|pos_num → pos_num → pos_num
|
||||
pos_num.no_confusion_type|Type → pos_num → pos_num → Type
|
||||
pos_num.no_confusion|eq ?v1 ?v2 → pos_num.no_confusion_type ?P ?v1 ?v2
|
||||
pos_num.lt|pos_num → pos_num → bool
|
||||
pos_num.rec_on|Π (n : pos_num), ?C pos_num.one → (Π (a : pos_num), ?C a → ?C (pos_num.bit1 a)) → (Π (a : pos_num), ?C a → ?C (pos_num.bit0 a)) → ?C n
|
||||
pos_num.brec_on|Π (n : pos_num), (Π (n : pos_num), pos_num.below n → ?C n) → ?C n
|
||||
pos_num.rec_on|Π n, ?C pos_num.one → (Π a, ?C a → ?C (pos_num.bit1 a)) → (Π a, ?C a → ?C (pos_num.bit0 a)) → ?C n
|
||||
pos_num.brec_on|Π n, (Π n, pos_num.below n → ?C n) → ?C n
|
||||
pos_num.add|pos_num → pos_num → pos_num
|
||||
pos_num_has_mul|has_mul pos_num
|
||||
pos_num|Type
|
||||
|
|
|
|||
|
|
@ -5,7 +5,7 @@
|
|||
@
|
||||
-- ACK
|
||||
-- TYPE|11|5
|
||||
∀ {A : Type} {a b c : A}, eq a b → eq b c → eq a c
|
||||
∀ {A} {a b c}, eq a b → eq b c → eq a c
|
||||
-- ACK
|
||||
-- IDENTIFIER|11|5
|
||||
eq.trans
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
inv_del.lean:15:2: error: 1 unsolved subgoal
|
||||
A : Type,
|
||||
P : vec A 1 → Type,
|
||||
H : Π (a : A), P (vone a),
|
||||
H : Π a, P (vone a),
|
||||
a : A
|
||||
⊢ P (vone a)
|
||||
inv_del.lean:15:2: error: failed to add declaration 'vec.eone' to environment, value has metavariables
|
||||
|
|
|
|||
|
|
@ -1,15 +1,15 @@
|
|||
let bool := Prop,
|
||||
and := λ (p q : bool), Π (c : bool), (p → q → c) → c,
|
||||
and_intro := λ (p q : bool) (H1 : p) (H2 : q) (c : bool) (H : p → q → c), H H1 H2
|
||||
and := λ p q, Π c, (p → q → c) → c,
|
||||
and_intro := λ p q H1 H2 c H, H H1 H2
|
||||
in and_intro :
|
||||
∀ (p q : Prop),
|
||||
p → q → (∀ (c : Prop), (p → q → c) → c)
|
||||
∀ p q,
|
||||
p → q → (∀ c, (p → q → c) → c)
|
||||
let1.lean:19:19: error: type mismatch at term
|
||||
λ (p q : Prop) (H1 : p) (H2 : q) (c : Prop) (H : p → q → c),
|
||||
λ p q H1 H2 c H,
|
||||
H H1 H2
|
||||
has type
|
||||
∀ (p q : Prop),
|
||||
p → q → (∀ (c : Prop), (p → q → c) → c)
|
||||
∀ p q,
|
||||
p → q → (∀ c, (p → q → c) → c)
|
||||
but is expected to have type
|
||||
∀ (p q : Prop),
|
||||
p → q → (λ (p q : Prop), ∀ (c : Prop), (p → q → c) → c) q p
|
||||
∀ p q,
|
||||
p → q → (λ p q, ∀ c, (p → q → c) → c) q p
|
||||
|
|
|
|||
|
|
@ -1,8 +1,8 @@
|
|||
definition test.foo.prf [irreducible] : ∀ (x : ℕ), 0 < succ (succ x) :=
|
||||
λ (x : ℕ), lt.step (zero_lt_succ x)
|
||||
λ x, lt.step (zero_lt_succ x)
|
||||
definition test.bla : ℕ → ℕ :=
|
||||
λ (a : ℕ), foo (succ (succ a)) (foo.prf a)
|
||||
λ a, foo (succ (succ a)) (foo.prf a)
|
||||
definition test.bla : ℕ → ℕ :=
|
||||
λ (a : ℕ), test.foo (succ (succ a)) (test.foo.prf a)
|
||||
λ a, test.foo (succ (succ a)) (test.foo.prf a)
|
||||
definition test.foo.prf : ∀ (x : ℕ), 0 < succ (succ x) :=
|
||||
λ (x : ℕ), lt.step (zero_lt_succ x)
|
||||
λ x, lt.step (zero_lt_succ x)
|
||||
|
|
|
|||
|
|
@ -1,15 +1,15 @@
|
|||
definition bla : ℕ → ℕ :=
|
||||
λ (a : ℕ), foo (succ (succ a)) (bla_2 a)
|
||||
λ a, foo (succ (succ a)) (bla_2 a)
|
||||
definition bla_1 : ∀ (x : ℕ), 0 < succ x :=
|
||||
λ (x : ℕ), zero_lt_succ x
|
||||
λ x, zero_lt_succ x
|
||||
definition bla_2 : ∀ (x : ℕ), 0 < succ (succ x) :=
|
||||
λ (x : ℕ), lt.step (bla_1 x)
|
||||
λ x, lt.step (bla_1 x)
|
||||
definition test_1 [irreducible] : ∀ (x : ℕ), 0 < succ x :=
|
||||
λ (x : ℕ), zero_lt_succ x
|
||||
λ x, zero_lt_succ x
|
||||
definition test_2 [reducible] : ∀ (x : ℕ), 0 < succ (succ x) :=
|
||||
λ (x : ℕ), lt.step (test_1 x)
|
||||
λ x, lt.step (test_1 x)
|
||||
definition tst_1 : ∀ (x : Type.{l_1}) (x_1 : x) (x_2 : list.{l_1} x),
|
||||
x_1 :: x_2 = nil.{l_1} → list.no_confusion_type.{0 l_1} false (x_1 :: x_2) nil.{l_1} :=
|
||||
λ (x : Type.{l_1}) (x_1 : x) (x_2 : list.{l_1} x), list.no_confusion.{0 l_1}
|
||||
λ x x_1 x_2, list.no_confusion.{0 l_1}
|
||||
definition tst : Π {A : Type.{l_1}}, A → list.{l_1} A → bool :=
|
||||
λ (A : Type.{l_1}) (a : A) (l : list.{l_1} A), voo.{(max 1 l_1)} (a :: l) nil.{l_1} (tst_1.{l_1} A a l)
|
||||
λ A a l, voo.{(max 1 l_1)} (a :: l) nil.{l_1} (tst_1.{l_1} A a l)
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
noncomp_theory.lean:4:0: error: definition 'f' is noncomputable, it depends on 'real.discrete_linear_ordered_field'
|
||||
noncomputable definition g : ℝ → ℝ → ℝ :=
|
||||
λ (a : ℝ), div (a + a)
|
||||
λ a, div (a + a)
|
||||
definition r : ℕ → ℕ :=
|
||||
λ (a : ℕ), a
|
||||
λ a, a
|
||||
|
|
|
|||
|
|
@ -1,4 +1,4 @@
|
|||
∃ (A : Type₁) (x y : A), x = y : Prop
|
||||
∃ (x : num), x = 0 : Prop
|
||||
Σ (x : num), x = 10 : Type₁
|
||||
Σ (A : Type₁), list A : Type₂
|
||||
∃ A x y, x = y : Prop
|
||||
∃ x, x = 0 : Prop
|
||||
Σ x, x = 10 : Type₁
|
||||
Σ A, list A : Type₂
|
||||
|
|
|
|||
|
|
@ -1,4 +1,4 @@
|
|||
omit.lean:5:7: error: invalid omit command, 'A' has not been included
|
||||
omit.lean:7:10: error: invalid include command, 'A' has already been included
|
||||
foo : Π (A : Type), A → A → (Π (B : Type), B → B)
|
||||
tst : Π (A : Type), A → A → Type → Type
|
||||
foo : Π A, A → A → (Π B, B → B)
|
||||
tst : Π A, A → A → Type → Type
|
||||
|
|
|
|||
|
|
@ -1,17 +1,17 @@
|
|||
id : Π {A : Type}, A → A
|
||||
id₂ : Π {A : Type}, A → A
|
||||
id : Π {A}, A → A
|
||||
id₂ : Π {A}, A → A
|
||||
foo1 : A → B → A
|
||||
foo2 : A → B → A
|
||||
foo3 : A → B → A
|
||||
foo4 : A → B → A
|
||||
foo1 : Π {A : Type} {B : Type}, A → B → A
|
||||
foo2 : Π {A : Type} (B : Type), A → B → A
|
||||
foo3 : Π (A : Type) {B : Type}, A → B → A
|
||||
foo4 : Π (A : Type) (B : Type), A → B → A
|
||||
boo1 : Π {A : Type} {B : Type}, A → B → A
|
||||
boo2 : Π {A : Type} (B : Type), A → B → A
|
||||
boo3 : Π (A : Type) {B : Type}, A → B → A
|
||||
boo4 : Π (A : Type) (B : Type), A → B → A
|
||||
foo1 : Π {A} {B}, A → B → A
|
||||
foo2 : Π {A} B, A → B → A
|
||||
foo3 : Π A {B}, A → B → A
|
||||
foo4 : Π A B, A → B → A
|
||||
boo1 : Π {A} {B}, A → B → A
|
||||
boo2 : Π {A} B, A → B → A
|
||||
boo3 : Π A {B}, A → B → A
|
||||
boo4 : Π A B, A → B → A
|
||||
param_binder_update.lean:70:12: error: invalid parameter binder type update, 'A' is a variable
|
||||
param_binder_update.lean:71:11: error: invalid variable binder type update, 'C' is not a variable
|
||||
param_binder_update.lean:72:12: error: invalid variable binder type update, 'C' is not a variable
|
||||
|
|
|
|||
|
|
@ -1,4 +1,4 @@
|
|||
foo1 : Π {A : Type} {B : Type}, A → B → A
|
||||
foo2 : Π {A : Type} (B : Type), A → B → A
|
||||
foo3 : Π (A : Type) {B : Type}, A → B → A
|
||||
foo4 : Π (A : Type) (B : Type), A → B → A
|
||||
foo1 : Π {A} {B}, A → B → A
|
||||
foo2 : Π {A} B, A → B → A
|
||||
foo3 : Π A {B}, A → B → A
|
||||
foo4 : Π A B, A → B → A
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
definition Sum_weird [forward] : ∀ (f g h : ℕ → ℕ) (n : ℕ), Sum n (λ (x : ℕ), f (g (h x))) = 1 :=
|
||||
λ (f g h : ℕ → ℕ) (n : ℕ), sorry
|
||||
λ f g h n, sorry
|
||||
(multi-)patterns:
|
||||
?M_1 : ℕ → ℕ, ?M_2 : ℕ → ℕ, ?M_3 : ℕ → ℕ, ?M_4 : ℕ
|
||||
{Sum ?M_4 (λ (x : ℕ), ?M_1 (?M_2 (?M_3 x)))}
|
||||
{Sum ?M_4 (λ x, ?M_1 (?M_2 (?M_3 x)))}
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
λ {A : Type} (B : Type) (a : A) (b : B), a : Π (B : Type), ?A → B → ?A
|
||||
λ {A B : Type} (a : A) (b : B), a : ?A → ?B → ?A
|
||||
λ (A : Type) {B : Type} (a : A) (b : B), a : Π (A : Type) {B : Type}, A → B → A
|
||||
λ (A B : Type) (a : A) (b : B), a : Π (A B : Type), A → B → A
|
||||
λ [A : Type] (B : Type) (a : A) (b : B), a : Π (B : Type), ?A → B → ?A
|
||||
λ ⦃A : Type⦄ {B : Type} (a : A) (b : B), a : Π ⦃A : Type⦄ {B : Type}, A → B → A
|
||||
λ ⦃A B : Type⦄ (a : A) (b : B), a : Π ⦃A B : Type⦄, A → B → A
|
||||
λ {A} B a b, a : Π B, ?A → B → ?A
|
||||
λ {A B} a b, a : ?A → ?B → ?A
|
||||
λ A {B} a b, a : Π A {B}, A → B → A
|
||||
λ A B a b, a : Π A B, A → B → A
|
||||
λ [A] B a b, a : Π B, ?A → B → ?A
|
||||
λ ⦃A⦄ {B} a b, a : Π ⦃A⦄ {B}, A → B → A
|
||||
λ ⦃A B⦄ a b, a : Π ⦃A B⦄, A → B → A
|
||||
|
|
|
|||
|
|
@ -1,6 +1,6 @@
|
|||
a + of_num b = 10 : Prop
|
||||
@eq.{1} nat
|
||||
(@add.{1} nat nat._trans_of_decidable_linear_ordered_semiring_2 ((λ (x : nat), x) a)
|
||||
(@add.{1} nat nat._trans_of_decidable_linear_ordered_semiring_2 ((λ x, x) a)
|
||||
(nat.of_num (@bit0.{1} num num_has_add (@one.{1} num num_has_one))))
|
||||
(@bit0.{1} nat nat._trans_of_decidable_linear_ordered_semiring_2
|
||||
(@bit1.{1} nat nat._trans_of_decidable_linear_ordered_semiring_22 nat._trans_of_decidable_linear_ordered_semiring_2
|
||||
|
|
|
|||
|
|
@ -1,2 +1,2 @@
|
|||
1 : ℕ
|
||||
(λ (x : ℕ), x) 1 : ℕ
|
||||
(λ x, x) 1 : ℕ
|
||||
|
|
|
|||
|
|
@ -1,3 +1 @@
|
|||
char.rec_on :
|
||||
Π (n : char),
|
||||
(Π (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : bool), ?C (char.mk a a_1 a_2 a_3 a_4 a_5 a_6 a_7)) → ?C n
|
||||
char.rec_on : Π n, (Π a a_1 a_2 a_3 a_4 a_5 a_6 a_7, ?C (char.mk a a_1 a_2 a_3 a_4 a_5 a_6 a_7)) → ?C n
|
||||
|
|
|
|||
|
|
@ -1,3 +1,3 @@
|
|||
quot.sound : ∀ {A : Type} [s : setoid A] {a b : A}, setoid.r a b → quot.mk a = quot.mk b
|
||||
classical.strong_indefinite_description : Π {A : Type} (P : A → Prop), nonempty A → {x : A | Exists P → P x}
|
||||
propext : ∀ {a b : Prop}, (a ↔ b) → a = b
|
||||
quot.sound : ∀ {A} [s] {a b}, setoid.r a b → quot.mk a = quot.mk b
|
||||
classical.strong_indefinite_description : Π {A} P, nonempty A → {x | Exists P → P x}
|
||||
propext : ∀ {a b}, (a ↔ b) → a = b
|
||||
|
|
|
|||
|
|
@ -1,3 +1,3 @@
|
|||
quot.sound : ∀ {A : Type} [s : setoid A] {a b : A}, setoid.r a b → quot.mk a = quot.mk b
|
||||
classical.strong_indefinite_description : Π {A : Type} (P : A → Prop), nonempty A → {x : A | Exists P → P x}
|
||||
propext : ∀ {a b : Prop}, (a ↔ b) → a = b
|
||||
quot.sound : ∀ {A} [s] {a b}, setoid.r a b → quot.mk a = quot.mk b
|
||||
classical.strong_indefinite_description : Π {A} P, nonempty A → {x | Exists P → P x}
|
||||
propext : ∀ {a b}, (a ↔ b) → a = b
|
||||
|
|
|
|||
|
|
@ -1,8 +1,8 @@
|
|||
no axioms
|
||||
------
|
||||
quot.sound : ∀ {A : Type} [s : setoid A] {a b : A}, setoid.r a b → quot.mk a = quot.mk b
|
||||
classical.strong_indefinite_description : Π {A : Type} (P : A → Prop), nonempty A → {x : A | Exists P → P x}
|
||||
propext : ∀ {a b : Prop}, (a ↔ b) → a = b
|
||||
quot.sound : ∀ {A} [s] {a b}, setoid.r a b → quot.mk a = quot.mk b
|
||||
classical.strong_indefinite_description : Π {A} P, nonempty A → {x | Exists P → P x}
|
||||
propext : ∀ {a b}, (a ↔ b) → a = b
|
||||
------
|
||||
theorem foo3 : 0 = 0 :=
|
||||
foo2
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
protected_test.lean:2:8: error: unknown identifier 'induction_on'
|
||||
protected_test.lean:3:8: error: unknown identifier 'rec_on'
|
||||
nat.induction_on : ∀ (n : ℕ), ?C 0 → (∀ (a : ℕ), ?C a → ?C (succ a)) → ?C n
|
||||
le.rec_on : le ?a ?a_1 → ?C ?a → (∀ {b : ℕ}, le ?a b → ?C b → ?C (succ b)) → ?C ?a_1
|
||||
le.rec_on : le ?a ?a_1 → ?C ?a → (∀ {b : ℕ}, le ?a b → ?C b → ?C (succ b)) → ?C ?a_1
|
||||
nat.induction_on : ∀ n, ?C 0 → (∀ a, ?C a → ?C (succ a)) → ?C n
|
||||
le.rec_on : le ?a ?a_1 → ?C ?a → (∀ {b}, le ?a b → ?C b → ?C (succ b)) → ?C ?a_1
|
||||
le.rec_on : le ?a ?a_1 → ?C ?a → (∀ {b}, le ?a b → ?C b → ?C (succ b)) → ?C ?a_1
|
||||
protected_test.lean:8:10: error: unknown identifier 'rec_on'
|
||||
le.rec_on : le ?a ?a_1 → ?C ?a → (∀ {b : ℕ}, le ?a b → ?C b → ?C (succ b)) → ?C ?a_1
|
||||
le.rec_on : le ?a ?a_1 → ?C ?a → (∀ {b}, le ?a b → ?C b → ?C (succ b)) → ?C ?a_1
|
||||
|
|
|
|||
|
|
@ -6,5 +6,5 @@ h₂ : b = c
|
|||
⊢ b = c
|
||||
pstate.lean:4:7: error: failed to add declaration 'foo' to environment, value has metavariables
|
||||
remark: set 'formatter.hide_full_terms' to false to see the complete term
|
||||
λ (A : Type) (a b c : A) (h₁ : …) (h₂ : …),
|
||||
λ A a b c h₁ h₂,
|
||||
eq.trans h₁ ?M_1
|
||||
|
|
|
|||
|
|
@ -1 +1 @@
|
|||
λ (x : A), f x
|
||||
λ x, f x
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
definition foo [forward] : ∀ (m n k : ℕ), P (f m) → P (g n) → P (f k) → P k ∧ R (g m) (f n) ∧ P (g m) ∧ P (f n) :=
|
||||
λ (m n k : ℕ), sorry
|
||||
λ m n k, sorry
|
||||
(multi-)patterns:
|
||||
?M_1 : ℕ, ?M_2 : ℕ, ?M_3 : ℕ
|
||||
{P ?M_3, R (g ?M_1) (f ?M_2)}
|
||||
|
|
|
|||
|
|
@ -32,4 +32,4 @@ replace_tac.lean:26:0: error: 1 unsolved subgoal
|
|||
⊢ f 4 = p
|
||||
replace_tac.lean:26:0: error: failed to add declaration 'example' to environment, value has metavariables
|
||||
remark: set 'formatter.hide_full_terms' to false to see the complete term
|
||||
?M_1
|
||||
?M_1
|
||||
|
|
|
|||
|
|
@ -1,4 +1,4 @@
|
|||
id2 : (A → B → A) → A
|
||||
id2 : (A → B → A) → A
|
||||
id2 : ?B a → (A → ?B a → A) → A
|
||||
id2 : ?A → (Π {B : Type}, B → (?A → B → ?A) → ?A)
|
||||
id2 : ?A → (Π {B}, B → (?A → B → ?A) → ?A)
|
||||
|
|
|
|||
|
|
@ -14,5 +14,5 @@ Hb : b
|
|||
⊢ b ∧ a
|
||||
show_tac.lean:7:0: error: failed to add declaration 'example' to environment, value has metavariables
|
||||
remark: set 'formatter.hide_full_terms' to false to see the complete term
|
||||
λ (a b : Prop) (Hab : …),
|
||||
λ a b Hab,
|
||||
?M_1
|
||||
|
|
|
|||
|
|
@ -1,2 +1,2 @@
|
|||
λ (a b c : bool), g y
|
||||
λ (a b c : bool), h z
|
||||
λ a b c, g y
|
||||
λ a b c, h z
|
||||
|
|
|
|||
|
|
@ -1,4 +1,4 @@
|
|||
H1
|
||||
imp_congr H1 H2
|
||||
imp_congr H1 (imp_congr H2 H3)
|
||||
forall_congr (λ (x : T), H x)
|
||||
forall_congr (λ x, H x)
|
||||
|
|
|
|||
|
|
@ -1,14 +1,14 @@
|
|||
x = y → true
|
||||
T → x = y → true
|
||||
∀ (a : T), x = a → a = y
|
||||
∀ (a : T), a = x → true
|
||||
∀ a, x = a → a = y
|
||||
∀ a, a = x → true
|
||||
T → T → x = y → true
|
||||
T → T → x = y → P y
|
||||
(∀ (x : T), P x ↔ Q x) → Q x
|
||||
Prop → (∀ (x : T), P x ↔ Q x) → Prop → Q x
|
||||
∀ (a : Prop), (∀ (x : T), P x ↔ Q x) → a ∨ Q x
|
||||
(∀ (x : T), P x ↔ Q x) → Q x
|
||||
∀ (a : T), T → (∀ (x : T), P x ↔ Q x) → Q a
|
||||
∀ (a a_1 : T), a = a_1 → P a_1
|
||||
∀ (a a_1 a_2 : T), a = a_1 → a_1 = a_2 → P a_2
|
||||
∀ (a a_1 : T), a = a_1 → (∀ (w : T), P w ↔ Q w) → Q a_1
|
||||
(∀ x, P x ↔ Q x) → Q x
|
||||
Prop → (∀ x, P x ↔ Q x) → Prop → Q x
|
||||
∀ a, (∀ x, P x ↔ Q x) → a ∨ Q x
|
||||
(∀ x, P x ↔ Q x) → Q x
|
||||
∀ a, T → (∀ x, P x ↔ Q x) → Q a
|
||||
∀ a a_1, a = a_1 → P a_1
|
||||
∀ a a_1 a_2, a = a_1 → a_1 = a_2 → P a_2
|
||||
∀ a a_1, a = a_1 → (∀ w, P w ↔ Q w) → Q a_1
|
||||
|
|
|
|||
|
|
@ -17,7 +17,7 @@ nonempty : Type → Prop
|
|||
point : Type → Type → Type
|
||||
setoid : Type → Type
|
||||
subsingleton : Type → Prop
|
||||
well_founded : Π {A : Type}, (A → A → Prop) → Prop
|
||||
well_founded : Π {A}, (A → A → Prop) → Prop
|
||||
decidable : Prop → Type₁
|
||||
has_add : Type → Type
|
||||
has_div : Type → Type
|
||||
|
|
@ -37,4 +37,4 @@ nonempty : Type → Prop
|
|||
point : Type → Type → Type
|
||||
setoid : Type → Type
|
||||
subsingleton : Type → Prop
|
||||
well_founded : Π {A : Type}, (A → A → Prop) → Prop
|
||||
well_founded : Π {A}, (A → A → Prop) → Prop
|
||||
|
|
|
|||
|
|
@ -1 +1 @@
|
|||
{x : ℕ | x > 0} : Type₁
|
||||
{x | x > 0} : Type₁
|
||||
|
|
|
|||
|
|
@ -1,3 +1,3 @@
|
|||
∃ (x : A), p x : bool
|
||||
∃ (x y : A), q x y : bool
|
||||
λ (x : A), x : A → A
|
||||
∃ x, p x : bool
|
||||
∃ x y, q x y : bool
|
||||
λ x, x : A → A
|
||||
|
|
|
|||
|
|
@ -1,2 +1,2 @@
|
|||
λ (f g : N → N → N) (x y : N), f x (g x y) : (N → N → N) → (N → N → N) → N → N → N
|
||||
λ f g x y, f x (g x y) : (N → N → N) → (N → N → N) → N → N → N
|
||||
t12.lean:7:7: error: invalid expression
|
||||
|
|
|
|||
|
|
@ -1,2 +1,2 @@
|
|||
[choice (g a b) (f a b)]
|
||||
λ (h : A → A → A), h a b : (A → A → A) → A
|
||||
λ h, h a b : (A → A → A) → A
|
||||
|
|
|
|||
|
|
@ -5,13 +5,13 @@ unfold_rec.lean:23:2: proof state
|
|||
n m : ℕ
|
||||
⊢ succ (n + succ m) = succ (succ (n + m))
|
||||
unfold_rec.lean:38:2: proof state
|
||||
fibgt0 : ∀ (b n c : ℕ), fib ℕ b n c > 0,
|
||||
fibgt0 : ∀ b n c, fib ℕ b n c > 0,
|
||||
b m c : ℕ
|
||||
⊢ fib ℕ b m c + fib ℕ b (succ m) c > 0
|
||||
unfold_rec.lean:47:2: proof state
|
||||
A : Type,
|
||||
B : Type,
|
||||
unzip_zip : ∀ {n : ℕ} (v₁ : vector A n) (v₂ : vector B n), unzip (zip v₁ v₂) = (v₁, v₂),
|
||||
unzip_zip : ∀ {n} v₁ v₂, unzip (zip v₁ v₂) = (v₁, v₂),
|
||||
m : ℕ,
|
||||
a : A,
|
||||
va : vector A m,
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
id1 : Π (A : Type.{u}), A → A
|
||||
id2.{l_2} : Π (B : Type.{l_2}), B → B
|
||||
id3.{l_2} : Π (C : Type.{l_2}), C → C
|
||||
foo.{l_2} : Π (A₁ A₂ : Type.{l_2}), A₁ → A₂ → Prop
|
||||
id1 : Π A, A → A
|
||||
id2.{l_2} : Π B, B → B
|
||||
id3.{l_2} : Π C, C → C
|
||||
foo.{l_2} : Π A₁ A₂, A₁ → A₂ → Prop
|
||||
Type.{m} : Type.{m+1}
|
||||
|
|
|
|||
|
|
@ -37,5 +37,5 @@ H₂ : b = c
|
|||
⊢ c = a
|
||||
unsolved_proof_qed.lean:5:0: error: failed to add declaration 'example' to environment, value has metavariables
|
||||
remark: set 'formatter.hide_full_terms' to false to see the complete term
|
||||
λ (a b c : ℕ) (H₁ : …) (H₂ : …),
|
||||
λ a b c H₁ H₂,
|
||||
… ?M_1
|
||||
|
|
|
|||
|
|
@ -1,9 +1,7 @@
|
|||
urec.lean:3:0: error: invalid user defined recursor, result type must be of the form (C t), where C is a bound variable, and t is a (possibly empty) sequence of bound variables
|
||||
urec.lean:5:0: error: invalid user defined recursor, 'nat.rec' is a builtin recursor
|
||||
urec.lean:19:0: error: invalid user defined recursor, type of the major premise 'a' must be for the form (I ...), where I is a constant
|
||||
myrec.{l_1 l_2} :
|
||||
Π (A : Type.{l_1}) (M : list.{l_1} A → Type.{l_2}) (l : list.{l_1} A),
|
||||
M (@nil.{l_1} A) → (Π (a : A), M [a]) → (Π (a₁ a₂ : A), M [a₁, a₂]) → M l
|
||||
myrec.{l_1 l_2} : Π A M l, M (@nil.{l_1} A) → (Π a, M [a]) → (Π a₁ a₂, M [a₁, a₂]) → M l
|
||||
recursor information
|
||||
num. parameters: 1
|
||||
num. indices: 0
|
||||
|
|
@ -24,10 +22,8 @@ recursor information
|
|||
major premise pos.: 2
|
||||
dep. elimination: 1
|
||||
vector.induction_on.{l_1} :
|
||||
∀ {A : Type.{l_1}} {C : Π (a : ℕ), vector.{l_1} A a → Prop} {a : ℕ} (n : vector.{l_1} A a),
|
||||
C 0 (@vector.nil.{l_1} A) →
|
||||
(∀ {n : ℕ} (a : A) (a_1 : vector.{l_1} A n), C n a_1 → C (nat.succ n) (@vector.cons.{l_1} A n a a_1)) →
|
||||
C a n
|
||||
∀ {A} {C} {a} n,
|
||||
C 0 (@vector.nil.{l_1} A) → (∀ {n} a a_1, C n a_1 → C (nat.succ n) (@vector.cons.{l_1} A n a a_1)) → C a n
|
||||
recursor information
|
||||
num. parameters: 1
|
||||
num. indices: 1
|
||||
|
|
@ -39,9 +35,7 @@ recursor information
|
|||
dep. elimination: 1
|
||||
parameters pos. at major: 1
|
||||
indices pos. at major: 2
|
||||
Exists.rec.{l_1} :
|
||||
∀ {A : Type.{l_1}} {P : A → Prop} {C : Prop},
|
||||
(∀ (a : A), P a → C) → @Exists.{l_1} A P → C
|
||||
Exists.rec.{l_1} : ∀ {A} {P} {C}, (∀ a, P a → C) → @Exists.{l_1} A P → C
|
||||
recursor information
|
||||
num. parameters: 2
|
||||
num. indices: 0
|
||||
|
|
|
|||
|
|
@ -1 +1 @@
|
|||
foo : Π (B : Type), B → (Π (A : Type), A → A = B → Prop)
|
||||
foo : Π B, B → (Π A, A → A = B → Prop)
|
||||
|
|
|
|||
|
|
@ -1,4 +1,4 @@
|
|||
succ (nat.rec 2 (λ (b₁ : ℕ), succ) 0)
|
||||
succ (nat.rec 2 (λ b₁, succ) 0)
|
||||
3
|
||||
succ (nat.rec a (λ (b₁ : ℕ), succ) 0)
|
||||
succ (nat.rec a (λ b₁, succ) 0)
|
||||
succ a
|
||||
|
|
|
|||
Loading…
Reference in a new issue