lean2/tests/lean/elab5.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: C
Assumed: D
Assumed: R
Proved: R2
Set: lean::pp::implicit
Import "basic"
Variable C {A B : Type} (H : @eq Type A B) (a : A) : B
Variable D {A A' : Type} {B : A → Type} {B' : A' → Type} (H : @eq Type (Π x : A, B x) (Π x : A', B' x)) :
@eq Type A A'
Variable R {A A' : Type} {B : A → Type} {B' : A' → Type} (H : @eq Type (Π x : A, B x) (Π x : A', B' x)) (a : A) :
@eq Type (B a) (B' (@C A A' (@D A A' (λ x : A, B x) (λ x : A', B' x) H) a))
Theorem R2 (A1 A2 B1 B2 : Type) (H : @eq Type (A1 → B1) (A2 → B2)) (a : A1) : @eq Type B1 B2 :=
@R A1 A2 (λ x : A1, B1) (λ x : A2, B2) H a