lean2/tests/lean/elab1.lean.expected.out

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Set: pp::colors
Set: pp::unicode
Assumed: f
Failed to solve
⊢ (?M::1 ≈ λ x : , x) ⊕ (?M::1 ≈ nat_to_int) ⊕ (?M::1 ≈ nat_to_real)
(line: 4: pos: 8) Coercion for
10
Failed to solve
⊢ Bool ≺
Substitution
⊢ Bool ≺ ?M::0
(line: 4: pos: 6) Type of argument 3 must be convertible to the expected type in the application of
@f
with arguments:
?M::0
?M::1 10
Assignment
≺ ?M::0
Substitution
⊢ ?M::5[inst:0 (10)] ≺ ?M::0
(line: 4: pos: 6) Type of argument 2 must be convertible to the expected type in the application of
@f
with arguments:
?M::0
?M::1 10
Assignment
x : ≈ ?M::5
Destruct/Decompose
≈ Π x : ?M::4, ?M::5
Substitution
⊢ ?M::3 ≈ Π x : ?M::4, ?M::5
Function expected at
?M::1 10
Assignment
≺ ?M::3
Propagate type, ?M::1 : ?M::3
Assignment
⊢ ?M::1 ≈ λ x : , x
Assumption 0
Failed to solve
⊢ Bool ≺
Substitution
⊢ Bool ≺ ?M::0
(line: 4: pos: 6) Type of argument 3 must be convertible to the expected type in the application of
@f
with arguments:
?M::0
?M::1 10
Assignment
≺ ?M::0
Substitution
⊢ ?M::5[inst:0 (10)] ≺ ?M::0
(line: 4: pos: 6) Type of argument 2 must be convertible to the expected type in the application of
@f
with arguments:
?M::0
?M::1 10
Assignment
a : ≈ ?M::5
Destruct/Decompose
≈ Π x : ?M::4, ?M::5
Substitution
⊢ ?M::3 ≈ Π x : ?M::4, ?M::5
Function expected at
?M::1 10
Assignment
≺ ?M::3
Propagate type, ?M::1 : ?M::3
Assignment
⊢ ?M::1 ≈ nat_to_int
Assumption 1
Failed to solve
⊢ Bool ≺
Substitution
⊢ Bool ≺ ?M::0
(line: 4: pos: 6) Type of argument 3 must be convertible to the expected type in the application of
@f
with arguments:
?M::0
?M::1 10
Assignment
≺ ?M::0
Substitution
⊢ ?M::5[inst:0 (10)] ≺ ?M::0
(line: 4: pos: 6) Type of argument 2 must be convertible to the expected type in the application of
@f
with arguments:
?M::0
?M::1 10
Assignment
a : ≈ ?M::5
Destruct/Decompose
≈ Π x : ?M::4, ?M::5
Substitution
⊢ ?M::3 ≈ Π x : ?M::4, ?M::5
Function expected at
?M::1 10
Assignment
≺ ?M::3
Propagate type, ?M::1 : ?M::3
Assignment
⊢ ?M::1 ≈ nat_to_real
Assumption 2
Assumed: g
Error (line: 7, pos: 8) invalid expression, it still contains metavariables after elaboration, metavariable: ?M::1, type:
Type
Assumed: h
Failed to solve
x : ?M::0, A : Type ⊢ ?M::0 ≺ A
(line: 11: pos: 27) Type of argument 2 must be convertible to the expected type in the application of
h
with arguments:
A
x
Assumed: my_eq
Failed to solve
A : Type, B : Type, a : ?M::0, b : ?M::1, C : Type ⊢ ?M::0[lift:0:3] ≺ C
(line: 15: pos: 51) Type of argument 2 must be convertible to the expected type in the application of
my_eq
with arguments:
C
a
b
Assumed: a
Assumed: b
Assumed: H
Failed to solve
⊢ ?M::0 ⇒ ?M::3 ∧ a ≺ b
Substitution
⊢ ?M::0 ⇒ ?M::1 ≺ b
(line: 20: pos: 18) Type of definition 't1' must be convertible to expected type.
Assignment
H1 : ?M::2 ⊢ ?M::3 ∧ a ≺ ?M::1
Substitution
H1 : ?M::2 ⊢ ?M::3 ∧ ?M::4 ≺ ?M::1
Destruct/Decompose
⊢ Π H1 : ?M::2, ?M::3 ∧ ?M::4 ≺ Π a : ?M::0, ?M::1
(line: 20: pos: 18) Type of argument 3 must be convertible to the expected type in the application of
@Discharge
with arguments:
?M::0
?M::1
λ H1 : ?M::2, Conj H1 (Conjunct1 H)
Assignment
H1 : ?M::2 ⊢ a ≺ ?M::4
Substitution
H1 : ?M::2 ⊢ ?M::5 ≺ ?M::4
(line: 20: pos: 37) Type of argument 4 must be convertible to the expected type in the application of
@Conj
with arguments:
?M::3
?M::4
H1
Conjunct1 H
Assignment
H1 : ?M::2 ⊢ a ≈ ?M::5
Destruct/Decompose
H1 : ?M::2 ⊢ a ∧ b ≺ ?M::5 ∧ ?M::6
(line: 20: pos: 45) Type of argument 3 must be convertible to the expected type in the application of
@Conjunct1
with arguments:
?M::5
?M::6
H
Failed to solve
⊢ b ≈ a
Substitution
⊢ b ≈ ?M::3
Destruct/Decompose
⊢ b == b ≺ ?M::3 == ?M::4
(line: 22: pos: 22) Type of argument 6 must be convertible to the expected type in the application of
@Trans
with arguments:
?M::1
?M::2
?M::3
?M::4
Refl a
Refl b
Assignment
⊢ a ≈ ?M::3
Destruct/Decompose
⊢ a == a ≺ ?M::2 == ?M::3
(line: 22: pos: 22) Type of argument 5 must be convertible to the expected type in the application of
@Trans
with arguments:
?M::1
?M::2
?M::3
?M::4
Refl a
Refl b
Failed to solve
⊢ (?M::1 ≈ Type) ⊕ (?M::1 ≈ Bool)
Destruct/Decompose
⊢ ?M::1 ≺ Type
(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
@f
with arguments:
?M::0
Bool
Bool
Failed to solve
⊢ (?M::0 ≈ Type) ⊕ (?M::0 ≈ (Type 1)) ⊕ (?M::0 ≈ (Type M)) ⊕ (?M::0 ≈ (Type U))
Destruct/Decompose
⊢ Type ≺ ?M::0
(line: 24: pos: 6) Type of argument 2 must be convertible to the expected type in the application of
@f
with arguments:
?M::0
Bool
Bool
Failed to solve
⊢ (Type 1) ≺ Type
Substitution
⊢ (Type 1) ≺ ?M::1
Propagate type, ?M::0 : ?M::1
Assignment
⊢ ?M::0 ≈ Type
Assumption 1
Assignment
⊢ ?M::1 ≈ Type
Assumption 0
Failed to solve
⊢ (Type 2) ≺ Type
Substitution
⊢ (Type 2) ≺ ?M::1
Propagate type, ?M::0 : ?M::1
Assignment
⊢ ?M::0 ≈ (Type 1)
Assumption 2
Assignment
⊢ ?M::1 ≈ Type
Assumption 0
Failed to solve
⊢ (Type M+1) ≺ Type
Substitution
⊢ (Type M+1) ≺ ?M::1
Propagate type, ?M::0 : ?M::1
Assignment
⊢ ?M::0 ≈ (Type M)
Assumption 3
Assignment
⊢ ?M::1 ≈ Type
Assumption 0
Failed to solve
⊢ (Type U+1) ≺ Type
Substitution
⊢ (Type U+1) ≺ ?M::1
Propagate type, ?M::0 : ?M::1
Assignment
⊢ ?M::0 ≈ (Type U)
Assumption 4
Assignment
⊢ ?M::1 ≈ Type
Assumption 0
Failed to solve
⊢ (?M::0 ≈ Type) ⊕ (?M::0 ≈ (Type 1)) ⊕ (?M::0 ≈ (Type M)) ⊕ (?M::0 ≈ (Type U))
Destruct/Decompose
⊢ Type ≺ ?M::0
(line: 24: pos: 6) Type of argument 2 must be convertible to the expected type in the application of
@f
with arguments:
?M::0
Bool
Bool
Failed to solve
⊢ (Type 1) ≺ Bool
Substitution
⊢ (Type 1) ≺ ?M::1
Propagate type, ?M::0 : ?M::1
Assignment
⊢ ?M::0 ≈ Type
Assumption 6
Assignment
⊢ ?M::1 ≈ Bool
Assumption 5
Failed to solve
⊢ (Type 2) ≺ Bool
Substitution
⊢ (Type 2) ≺ ?M::1
Propagate type, ?M::0 : ?M::1
Assignment
⊢ ?M::0 ≈ (Type 1)
Assumption 7
Assignment
⊢ ?M::1 ≈ Bool
Assumption 5
Failed to solve
⊢ (Type M+1) ≺ Bool
Substitution
⊢ (Type M+1) ≺ ?M::1
Propagate type, ?M::0 : ?M::1
Assignment
⊢ ?M::0 ≈ (Type M)
Assumption 8
Assignment
⊢ ?M::1 ≈ Bool
Assumption 5
Failed to solve
⊢ (Type U+1) ≺ Bool
Substitution
⊢ (Type U+1) ≺ ?M::1
Propagate type, ?M::0 : ?M::1
Assignment
⊢ ?M::0 ≈ (Type U)
Assumption 9
Assignment
⊢ ?M::1 ≈ Bool
Assumption 5
Failed to solve
a : Bool, b : Bool, H : ?M::2, H_a : ?M::6 ⊢ (a ⇒ b) ⇒ a ≺ a
Substitution
a : Bool, b : Bool, H : ?M::2, H_a : ?M::6 ⊢ (a ⇒ b) ⇒ a ≺ ?M::5[lift:0:1]
Substitution
a : Bool, b : Bool, H : ?M::2, H_a : ?M::6 ⊢ ?M::2[lift:0:2] ≺ ?M::5[lift:0:1]
Destruct/Decompose
a : Bool, b : Bool, H : ?M::2 ⊢ Π H_a : ?M::6, ?M::2[lift:0:2] ≺ Π a : ?M::3, ?M::5[lift:0:1]
(line: 27: pos: 21) Type of argument 5 must be convertible to the expected type in the application of
@DisjCases
with arguments:
?M::3
?M::4
?M::5
EM a
λ H_a : ?M::6, H
λ H_na : ?M::7, NotImp1 (MT H H_na)
Normalize assignment
?M::0
Assignment
a : Bool, b : Bool ⊢ ?M::2 ≈ ?M::0
Destruct/Decompose
a : Bool, b : Bool ⊢ Π H : ?M::2, ?M::5 ≺ Π a : ?M::0, ?M::1[lift:0:1]
(line: 27: pos: 4) Type of argument 3 must be convertible to the expected type in the application of
@Discharge
with arguments:
?M::0
?M::1
λ H : ?M::2, DisjCases (EM a) (λ H_a : ?M::6, H) (λ H_na : ?M::7, NotImp1 (MT H H_na))
Assignment
a : Bool, b : Bool ⊢ ?M::0 ≈ (a ⇒ b) ⇒ a
Destruct/Decompose
a : Bool, b : Bool ⊢ ?M::0 ⇒ ?M::1 ≺ ((a ⇒ b) ⇒ a) ⇒ a
Destruct/Decompose
a : Bool ⊢ Π b : Bool, ?M::0 ⇒ ?M::1 ≺ Π b : Bool, ((a ⇒ b) ⇒ a) ⇒ a
Destruct/Decompose
⊢ Π a b : Bool, ?M::0 ⇒ ?M::1 ≺ Π a b : Bool, ((a ⇒ b) ⇒ a) ⇒ a
(line: 26: pos: 16) Type of definition 'pierce' must be convertible to expected type.
Assignment
a : Bool, b : Bool, H : ?M::2 ⊢ ?M::5 ≺ a
Substitution
a : Bool, b : Bool, H : ?M::2 ⊢ ?M::5 ≺ ?M::1[lift:0:1]
Destruct/Decompose
a : Bool, b : Bool ⊢ Π H : ?M::2, ?M::5 ≺ Π a : ?M::0, ?M::1[lift:0:1]
(line: 27: pos: 4) Type of argument 3 must be convertible to the expected type in the application of
@Discharge
with arguments:
?M::0
?M::1
λ H : ?M::2, DisjCases (EM a) (λ H_a : ?M::6, H) (λ H_na : ?M::7, NotImp1 (MT H H_na))
Assignment
a : Bool, b : Bool ⊢ ?M::1 ≈ a
Destruct/Decompose
a : Bool, b : Bool ⊢ ?M::0 ⇒ ?M::1 ≺ ((a ⇒ b) ⇒ a) ⇒ a
Destruct/Decompose
a : Bool ⊢ Π b : Bool, ?M::0 ⇒ ?M::1 ≺ Π b : Bool, ((a ⇒ b) ⇒ a) ⇒ a
Destruct/Decompose
⊢ Π a b : Bool, ?M::0 ⇒ ?M::1 ≺ Π a b : Bool, ((a ⇒ b) ⇒ a) ⇒ a
(line: 26: pos: 16) Type of definition 'pierce' must be convertible to expected type.