test(tests/lean/run): add basic ematching tests

This commit is contained in:
Leonardo de Moura 2015-11-30 10:33:00 -07:00
parent 08bb966581
commit 5844e96734
2 changed files with 57 additions and 0 deletions

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import data.nat
open nat
constant f : nat → nat
constant g : nat → nat
definition lemma1 [forward] : ∀ x, g (f x) = x :=
sorry
set_option blast.ematch true
example (a b : nat) : f a = f b → a = b :=
by blast

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import algebra.ring data.nat
open algebra
variables {A : Type}
section
variables [s : add_comm_monoid A]
include s
attribute add.comm [forward]
attribute add.assoc [forward]
set_option blast.simp false
set_option blast.subst false
set_option blast.ematch true
theorem add_comm_three (a b c : A) : a + b + c = c + b + a :=
by blast
theorem add.comm4 : ∀ (n m k l : A), n + m + (k + l) = n + k + (m + l) :=
by blast
end
section
variable [s : group A]
include s
attribute mul.assoc [forward]
attribute mul.left_inv [forward]
attribute one_mul [forward]
set_option blast.simp false
set_option blast.subst false
set_option blast.ematch true
theorem inv_mul_cancel_left (a b : A) : a⁻¹ * (a * b) = b :=
by blast
attribute mul_one [forward]
attribute inv_mul_cancel_right [forward]
-- TODO(Leo): check if qfc can get this one
-- theorem inv_eq_of_mul_eq_one {a b : A} (H : a * b = 1) : a⁻¹ = b :=
-- by blast
end