lean2/tests/lean/tst6.lean
Leonardo de Moura a341643335 Fix unit tests for Windows
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-09-03 10:44:51 -07:00

58 lines
2.1 KiB
Text
Raw Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

Variable N : Type
Variable h : N -> N -> N
Theorem CongrH {a1 a2 b1 b2 : N} (H1 : a1 = b1) (H2 : a2 = b2) : (h a1 a2) = (h b1 b2) :=
Congr (Congr (Refl h) H1) H2
(* Display the theorem showing implicit arguments *)
Set lean::pp::implicit true
Show Environment 2
(* Display the theorem hiding implicit arguments *)
Set lean::pp::implicit false
Show Environment 2
Theorem Example1 (a b c d : N) (H: (a = b ∧ b = c) (a = d ∧ d = c)) : (h a b) = (h c b) :=
DisjCases H
(fun H1 : a = b ∧ b = c,
CongrH (Trans (Conjunct1 H1) (Conjunct2 H1)) (Refl b))
(fun H1 : a = d ∧ d = c,
CongrH (Trans (Conjunct1 H1) (Conjunct2 H1)) (Refl b))
(* Show proof of the last theorem with all implicit arguments *)
Set lean::pp::implicit true
Show Environment 1
(* Using placeholders to hide the type of H1 *)
Theorem Example2 (a b c d : N) (H: (a = b ∧ b = c) (a = d ∧ d = c)) : (h a b) = (h c b) :=
DisjCases H
(fun H1 : _,
CongrH (Trans (Conjunct1 H1) (Conjunct2 H1)) (Refl b))
(fun H1 : _,
CongrH (Trans (Conjunct1 H1) (Conjunct2 H1)) (Refl b))
Set lean::pp::implicit true
Show Environment 1
(* Same example but the first conjuct has unnecessary stuff *)
Theorem Example3 (a b c d e : N) (H: (a = b ∧ b = e ∧ b = c) (a = d ∧ d = c)) : (h a b) = (h c b) :=
DisjCases H
(fun H1 : _,
CongrH (Trans (Conjunct1 H1) (Conjunct2 (Conjunct2 H1))) (Refl b))
(fun H1 : _,
CongrH (Trans (Conjunct1 H1) (Conjunct2 H1)) (Refl b))
Set lean::pp::implicit false
Show Environment 1
Theorem Example4 (a b c d e : N) (H: (a = b ∧ b = e ∧ b = c) (a = d ∧ d = c)) : (h a c) = (h c a) :=
DisjCases H
(fun H1 : _,
let AeqC := Trans (Conjunct1 H1) (Conjunct2 (Conjunct2 H1))
in CongrH AeqC (Symm AeqC))
(fun H1 : _,
let AeqC := Trans (Conjunct1 H1) (Conjunct2 H1)
in CongrH AeqC (Symm AeqC))
Set lean::pp::implicit false
Show Environment 1