test(tests/lean): add Jeremy's proof to test suite

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2014-01-28 16:05:46 -08:00
parent b6985bd713
commit 72c607846a
2 changed files with 33 additions and 0 deletions

25
tests/lean/j1.lean Normal file
View file

@ -0,0 +1,25 @@
import tactic
import macros
definition bracket (A : Type) : Bool :=
∀ p : Bool, (A → p) → p
rewrite_set basic
add_rewrite imp_truel imp_truer imp_id eq_id : basic
set_option simp_tac::assumptions false
theorem bracket_eq (x : Bool) : bracket x = x
:= boolext
(assume H : ∀ p : Bool, (x → p) → p,
(have ((x → x) → x) = x : by simp basic) ◂ H x)
(assume H : x,
take p,
assume Hxp : x → p,
Hxp H)
add_rewrite bracket_eq eq_id
theorem coerce (a b : Bool) (H : @eq Type a b) : @eq Bool a b
:= calc a = bracket a : by simp
... = bracket b : @subst Type a b (λ x : Type, bracket a = bracket x) (refl (bracket a)) H
... = b : by simp

View file

@ -0,0 +1,8 @@
Set: pp::colors
Set: pp::unicode
Imported 'tactic'
Imported 'macros'
Defined: bracket
Set: simp_tac::assumptions
Proved: bracket_eq
Proved: coerce