lean2/tests/lean/interactive/t12.lean.expected.out

52 lines
1.5 KiB
Text
Raw Normal View History

# Set: pp::colors
Set: pp::unicode
Proved: T1
theorem T1 (A B : Bool) (assumption : A ∧ B) : B ∧ A :=
let lemma1 : A := and::eliml assumption, lemma2 : B := and::elimr assumption in and::intro lemma2 lemma1
# Proof state:
A : Bool, B : Bool, assumption : A ∧ B ⊢ A
## Proof state:
no goals
## Proof state:
A : Bool, B : Bool, assumption : A ∧ B, lemma1 : A ⊢ B
## Proof state:
no goals
## Proof state:
A : Bool, B : Bool, assumption : A ∧ B, lemma1 : A, lemma2 : B ⊢ B ∧ A
## Proof state:
no goals
## Proved: T2
# Proof state:
A : Bool, B : Bool, assumption : A ∧ B ⊢ A
## Proof state:
A : Bool, B : Bool, assumption::1 : A, assumption::2 : B ⊢ A
## Proof state:
no goals
## Proof state:
A : Bool, B : Bool, assumption : A ∧ B, lemma1 : A ⊢ B
## Proof state:
A : Bool, B : Bool, assumption::1 : A, assumption::2 : B, lemma1 : A ⊢ B
## Proof state:
no goals
## Proof state:
A : Bool, B : Bool, assumption : A ∧ B, lemma1 : A, lemma2 : B ⊢ B ∧ A
## Proof state:
A : Bool, B : Bool, assumption : A ∧ B, lemma1 : A, lemma2 : B ⊢ B
A : Bool, B : Bool, assumption : A ∧ B, lemma1 : A, lemma2 : B ⊢ A
## Proof state:
no goals
## Proved: T3
# Proof state:
A : Bool, B : Bool, assumption : A ∧ B ⊢ A
## Proof state:
A : Bool, B : Bool, assumption::1 : A, assumption::2 : B ⊢ A
## Proof state:
no goals
## Proof state:
A : Bool, B : Bool, assumption : A ∧ B, lemma1 : A ⊢ B
## Proof state:
A : Bool, B : Bool, assumption::1 : A, assumption::2 : B, lemma1 : A ⊢ B
## Proof state:
no goals
## Proved: T4
#