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lean2/tests/lean/bug.lean.expected.out
Leonardo de Moura 411ebbc3c1 refactor(library/basic_thms): move the proof of all basic theorems to a .Lean file 
This commit also adds several new theorems that are useful for implementing the simplifier.
TODO: perhaps we should remove the declarations at basic_thms.h?

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-12-29 03:04:49 -08:00

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Set: pp::colors
Set: pp::unicode
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢
(?M::3 ≈ (Type U)) ⊕ (?M::3 ≈ (Type M)) ⊕ (?M::3 ≈ (Type 1)) ⊕ (?M::3 ≈ Type) ⊕ (?M::3 ≈ Bool)
Destruct/Decompose
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::3 ≺ (Type U)
Normalize
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::3 ≺ TypeU
(line: 1: pos: 44) Type of argument 1 must be convertible to the expected type in the application of
@Symm
with arguments:
?M::0
?M::1
?M::2
H
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (?M::5 ≈ (Type U)) ⊕ (?M::5 ≈ (Type U+1))
Destruct/Decompose
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U) ≺ ?M::5
Propagate type, ?M::2 : ?M::5
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ A' ≈ ?M::2
Destruct/Decompose
A : (Type U), A' : (Type U), H : A == A' ⊢ A == A' ≺ ?M::1 == ?M::2
(line: 1: pos: 44) Type of argument 4 must be convertible to the expected type in the application of
@Symm
with arguments:
?M::0
?M::1
?M::2
H
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (?M::0 ≈ (Type U)) ⊕ (?M::0 ≈ (Type U+1))
Destruct/Decompose
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U) ≺ ?M::0
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::5 ≺ ?M::0
(line: 1: pos: 44) Type of argument 3 must be convertible to the expected type in the application of
@Symm
with arguments:
?M::0
?M::1
?M::2
H
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::5 ≈ (Type U)
Assumption 1
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+1) ≺ (Type U)
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+1) ≺ ?M::3
Propagate type, ?M::0 : ?M::3
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::0 ≈ (Type U)
Assumption 3
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::3 ≈ (Type U)
Assumption 0
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+2) ≺ (Type U)
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+2) ≺ ?M::3
Propagate type, ?M::0 : ?M::3
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::0 ≈ (Type U+1)
Assumption 4
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::3 ≈ (Type U)
Assumption 0
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (?M::0 ≈ (Type U+1)) ⊕ (?M::0 ≈ (Type U+2))
Destruct/Decompose
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+1) ≺ ?M::0
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::5 ≺ ?M::0
(line: 1: pos: 44) Type of argument 3 must be convertible to the expected type in the application of
@Symm
with arguments:
?M::0
?M::1
?M::2
H
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::5 ≈ (Type U+1)
Assumption 5
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+2) ≺ (Type U)
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+2) ≺ ?M::3
Propagate type, ?M::0 : ?M::3
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::0 ≈ (Type U+1)
Assumption 7
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::3 ≈ (Type U)
Assumption 0
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+3) ≺ (Type U)
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+3) ≺ ?M::3
Propagate type, ?M::0 : ?M::3
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::0 ≈ (Type U+2)
Assumption 8
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::3 ≈ (Type U)
Assumption 0
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (?M::5 ≈ (Type U)) ⊕ (?M::5 ≈ (Type U+1))
Destruct/Decompose
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U) ≺ ?M::5
Propagate type, ?M::2 : ?M::5
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ A' ≈ ?M::2
Destruct/Decompose
A : (Type U), A' : (Type U), H : A == A' ⊢ A == A' ≺ ?M::1 == ?M::2
(line: 1: pos: 44) Type of argument 4 must be convertible to the expected type in the application of
@Symm
with arguments:
?M::0
?M::1
?M::2
H
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (?M::0 ≈ (Type U)) ⊕ (?M::0 ≈ (Type U+1))
Destruct/Decompose
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U) ≺ ?M::0
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::5 ≺ ?M::0
(line: 1: pos: 44) Type of argument 3 must be convertible to the expected type in the application of
@Symm
with arguments:
?M::0
?M::1
?M::2
H
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::5 ≈ (Type U)
Assumption 10
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+1) ≺ (Type M)
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+1) ≺ ?M::3
Propagate type, ?M::0 : ?M::3
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::0 ≈ (Type U)
Assumption 12
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::3 ≈ (Type M)
Assumption 9
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+2) ≺ (Type M)
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+2) ≺ ?M::3
Propagate type, ?M::0 : ?M::3
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::0 ≈ (Type U+1)
Assumption 13
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::3 ≈ (Type M)
Assumption 9
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (?M::0 ≈ (Type U+1)) ⊕ (?M::0 ≈ (Type U+2))
Destruct/Decompose
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+1) ≺ ?M::0
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::5 ≺ ?M::0
(line: 1: pos: 44) Type of argument 3 must be convertible to the expected type in the application of
@Symm
with arguments:
?M::0
?M::1
?M::2
H
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::5 ≈ (Type U+1)
Assumption 14
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+2) ≺ (Type M)
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+2) ≺ ?M::3
Propagate type, ?M::0 : ?M::3
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::0 ≈ (Type U+1)
Assumption 16
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::3 ≈ (Type M)
Assumption 9
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+3) ≺ (Type M)
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+3) ≺ ?M::3
Propagate type, ?M::0 : ?M::3
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::0 ≈ (Type U+2)
Assumption 17
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::3 ≈ (Type M)
Assumption 9
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (?M::5 ≈ (Type U)) ⊕ (?M::5 ≈ (Type U+1))
Destruct/Decompose
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U) ≺ ?M::5
Propagate type, ?M::2 : ?M::5
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ A' ≈ ?M::2
Destruct/Decompose
A : (Type U), A' : (Type U), H : A == A' ⊢ A == A' ≺ ?M::1 == ?M::2
(line: 1: pos: 44) Type of argument 4 must be convertible to the expected type in the application of
@Symm
with arguments:
?M::0
?M::1
?M::2
H
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (?M::0 ≈ (Type U)) ⊕ (?M::0 ≈ (Type U+1))
Destruct/Decompose
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U) ≺ ?M::0
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::5 ≺ ?M::0
(line: 1: pos: 44) Type of argument 3 must be convertible to the expected type in the application of
@Symm
with arguments:
?M::0
?M::1
?M::2
H
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::5 ≈ (Type U)
Assumption 19
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+1) ≺ (Type 1)
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+1) ≺ ?M::3
Propagate type, ?M::0 : ?M::3
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::0 ≈ (Type U)
Assumption 21
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::3 ≈ (Type 1)
Assumption 18
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+2) ≺ (Type 1)
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+2) ≺ ?M::3
Propagate type, ?M::0 : ?M::3
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::0 ≈ (Type U+1)
Assumption 22
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::3 ≈ (Type 1)
Assumption 18
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (?M::0 ≈ (Type U+1)) ⊕ (?M::0 ≈ (Type U+2))
Destruct/Decompose
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+1) ≺ ?M::0
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::5 ≺ ?M::0
(line: 1: pos: 44) Type of argument 3 must be convertible to the expected type in the application of
@Symm
with arguments:
?M::0
?M::1
?M::2
H
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::5 ≈ (Type U+1)
Assumption 23
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+2) ≺ (Type 1)
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+2) ≺ ?M::3
Propagate type, ?M::0 : ?M::3
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::0 ≈ (Type U+1)
Assumption 25
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::3 ≈ (Type 1)
Assumption 18
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+3) ≺ (Type 1)
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+3) ≺ ?M::3
Propagate type, ?M::0 : ?M::3
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::0 ≈ (Type U+2)
Assumption 26
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::3 ≈ (Type 1)
Assumption 18
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (?M::5 ≈ (Type U)) ⊕ (?M::5 ≈ (Type U+1))
Destruct/Decompose
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U) ≺ ?M::5
Propagate type, ?M::2 : ?M::5
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ A' ≈ ?M::2
Destruct/Decompose
A : (Type U), A' : (Type U), H : A == A' ⊢ A == A' ≺ ?M::1 == ?M::2
(line: 1: pos: 44) Type of argument 4 must be convertible to the expected type in the application of
@Symm
with arguments:
?M::0
?M::1
?M::2
H
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (?M::0 ≈ (Type U)) ⊕ (?M::0 ≈ (Type U+1))
Destruct/Decompose
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U) ≺ ?M::0
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::5 ≺ ?M::0
(line: 1: pos: 44) Type of argument 3 must be convertible to the expected type in the application of
@Symm
with arguments:
?M::0
?M::1
?M::2
H
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::5 ≈ (Type U)
Assumption 28
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+1) ≺ Type
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+1) ≺ ?M::3
Propagate type, ?M::0 : ?M::3
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::0 ≈ (Type U)
Assumption 30
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::3 ≈ Type
Assumption 27
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+2) ≺ Type
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+2) ≺ ?M::3
Propagate type, ?M::0 : ?M::3
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::0 ≈ (Type U+1)
Assumption 31
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::3 ≈ Type
Assumption 27
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (?M::0 ≈ (Type U+1)) ⊕ (?M::0 ≈ (Type U+2))
Destruct/Decompose
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+1) ≺ ?M::0
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::5 ≺ ?M::0
(line: 1: pos: 44) Type of argument 3 must be convertible to the expected type in the application of
@Symm
with arguments:
?M::0
?M::1
?M::2
H
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::5 ≈ (Type U+1)
Assumption 32
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+2) ≺ Type
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+2) ≺ ?M::3
Propagate type, ?M::0 : ?M::3
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::0 ≈ (Type U+1)
Assumption 34
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::3 ≈ Type
Assumption 27
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+3) ≺ Type
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+3) ≺ ?M::3
Propagate type, ?M::0 : ?M::3
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::0 ≈ (Type U+2)
Assumption 35
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::3 ≈ Type
Assumption 27
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (?M::5 ≈ (Type U)) ⊕ (?M::5 ≈ (Type U+1))
Destruct/Decompose
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U) ≺ ?M::5
Propagate type, ?M::2 : ?M::5
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ A' ≈ ?M::2
Destruct/Decompose
A : (Type U), A' : (Type U), H : A == A' ⊢ A == A' ≺ ?M::1 == ?M::2
(line: 1: pos: 44) Type of argument 4 must be convertible to the expected type in the application of
@Symm
with arguments:
?M::0
?M::1
?M::2
H
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (?M::0 ≈ (Type U)) ⊕ (?M::0 ≈ (Type U+1))
Destruct/Decompose
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U) ≺ ?M::0
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::5 ≺ ?M::0
(line: 1: pos: 44) Type of argument 3 must be convertible to the expected type in the application of
@Symm
with arguments:
?M::0
?M::1
?M::2
H
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::5 ≈ (Type U)
Assumption 37
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+1) ≺ Bool
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+1) ≺ ?M::3
Propagate type, ?M::0 : ?M::3
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::0 ≈ (Type U)
Assumption 39
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::3 ≈ Bool
Assumption 36
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+2) ≺ Bool
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+2) ≺ ?M::3
Propagate type, ?M::0 : ?M::3
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::0 ≈ (Type U+1)
Assumption 40
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::3 ≈ Bool
Assumption 36
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (?M::0 ≈ (Type U+1)) ⊕ (?M::0 ≈ (Type U+2))
Destruct/Decompose
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+1) ≺ ?M::0
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::5 ≺ ?M::0
(line: 1: pos: 44) Type of argument 3 must be convertible to the expected type in the application of
@Symm
with arguments:
?M::0
?M::1
?M::2
H
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::5 ≈ (Type U+1)
Assumption 41
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+2) ≺ Bool
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+2) ≺ ?M::3
Propagate type, ?M::0 : ?M::3
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::0 ≈ (Type U+1)
Assumption 43
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::3 ≈ Bool
Assumption 36
Failed to solve
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+3) ≺ Bool
Substitution
A : (Type U), A' : (Type U), H : A == A' ⊢ (Type U+3) ≺ ?M::3
Propagate type, ?M::0 : ?M::3
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::0 ≈ (Type U+2)
Assumption 44
Assignment
A : (Type U), A' : (Type U), H : A == A' ⊢ ?M::3 ≈ Bool
Assumption 36
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