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feat(library/init/logic): make sure standard library can be compiled when proofs are erased

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Leonardo de Moura 2015-07-29 15:00:50 -07:00
parent bbd6946a15
commit 82836fe9e0
1 changed files with 9 additions and 7 deletions
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library/init/logic.lean
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@ -169,13 +169,6 @@ open eq.ops
theorem eq_rec_heq {A : Type} {P : A → Type} {a a' : A} (H : a = a') (p : P a) : H ▹ p == p := theorem eq_rec_heq {A : Type} {P : A → Type} {a a' : A} (H : a = a') (p : P a) : H ▹ p == p :=
eq.drec_on H !heq.refl eq.drec_on H !heq.refl
theorem eq_rec_of_heq_left : ∀ {A₁ A₂ : Type} {a₁ : A₁} {a₂ : A₂} (h : a₁ == a₂), heq.type_eq h ▹ a₁ = a₂
| A A a a (heq.refl a) := rfl
reveal eq.symm
theorem eq_rec_of_heq_right : ∀ {A₁ A₂ : Type} {a₁ : A₁} {a₂ : A₂} (h : a₁ == a₂), a₁ = (heq.type_eq h)⁻¹ ▹ a₂
| A A a a (heq.refl a) := rfl
theorem heq_of_eq_rec_left {A : Type} {P : A → Type} : ∀ {a a' : A} {p₁ : P a} {p₂ : P a'} (e : a = a') (h₂ : e ▹ p₁ = p₂), p₁ == p₂ theorem heq_of_eq_rec_left {A : Type} {P : A → Type} : ∀ {a a' : A} {p₁ : P a} {p₂ : P a'} (e : a = a') (h₂ : e ▹ p₁ = p₂), p₁ == p₂
| a a p₁ p₂ (eq.refl a) h := eq.rec_on h !heq.refl | a a p₁ p₂ (eq.refl a) h := eq.rec_on h !heq.refl
@ -190,6 +183,15 @@ theorem eq_rec_compose : ∀ {A B C : Type} (p₁ : B = C) (p₂ : A = B) (a : A
eq.refl A ▹ eq.refl A ▹ a = eq.refl A ▹ a : rfl eq.refl A ▹ eq.refl A ▹ a = eq.refl A ▹ a : rfl
... = (eq.refl A ⬝ eq.refl A) ▹ a : {proof_irrel (eq.refl A) (eq.refl A ⬝ eq.refl A)} ... = (eq.refl A ⬝ eq.refl A) ▹ a : {proof_irrel (eq.refl A) (eq.refl A ⬝ eq.refl A)}
theorem eq_rec_eq_eq_rec {A₁ A₂ : Type} {p : A₁ = A₂} : ∀ {a₁ : A₁} {a₂ : A₂}, p ▹ a₁ = a₂ → a₁ = p⁻¹ ▹ a₂ :=
eq.drec_on p (λ a₁ a₂ h, eq.drec_on h rfl)
theorem eq_rec_of_heq_left : ∀ {A₁ A₂ : Type} {a₁ : A₁} {a₂ : A₂} (h : a₁ == a₂), heq.type_eq h ▹ a₁ = a₂
| A A a a (heq.refl a) := rfl
theorem eq_rec_of_heq_right {A₁ A₂ : Type} {a₁ : A₁} {a₂ : A₂} (h : a₁ == a₂) : a₁ = (heq.type_eq h)⁻¹ ▹ a₂ :=
eq_rec_eq_eq_rec (eq_rec_of_heq_left h)
attribute heq.refl [refl] attribute heq.refl [refl]
attribute heq.trans [trans] attribute heq.trans [trans]
attribute heq.of_heq_of_eq [trans] attribute heq.of_heq_of_eq [trans]