lean2/tests/lean/tst4.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
Assumed: f
Assumed: N
Assumed: n1
Assumed: n2
Set: lean::pp::implicit
@f N n1 n2
@f ((N → N) → N → N) (λ x : N → N, x) (λ y : N → N, y)
Assumed: EqNice
@EqNice N n1 n2
@f N n1 n2 : N
@Congr : Π (A : TypeU) (B : A → TypeU) (f g : Π x : A, B x) (a b : A), f == g → a == b → f a == g b
@f N n1 n2
Assumed: a
Assumed: b
Assumed: c
Assumed: g
Assumed: H1
Proved: Pr
Axiom H1 : @eq N a b ∧ @eq N b c
Theorem Pr : @eq N (g a) (g c) :=
@Congr N
(λ x : N, N)
g
g
a
c
(@Refl (N → N) g)
(@Trans N a b c (@Conjunct1 (@eq N a b) (@eq N b c) H1) (@Conjunct2 (@eq N a b) (@eq N b c) H1))