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test(tests/lean/run): add another simple test

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Leonardo de Moura 2015-04-01 15:49:01 -07:00
parent bf142f3f18
commit f8023403af
1 changed files with 15 additions and 0 deletions
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tests/lean/run/finset.lean
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@ -175,4 +175,19 @@ namespace finset
example : to_finset [(1:nat), 1, 4, 2, 3] ≠ to_finset [2, 3, 1, 2, 2, 3] :=
dec_trivial
definition clean {A : Type} [H : decidable_eq A] (s : finset A) : finset A :=
quot.lift_on s (λ l, ⟦norep l⟧)
(λ l₁ l₂ e, calc
⟦norep l₁⟧ = ⟦l₁⟧ : quot.sound (eqv_norep l₁)
... = ⟦l₂⟧ : quot.sound e
... = ⟦norep l₂⟧ : quot.sound (eqv_norep l₂))
theorem eq_clean {A : Type} [H : decidable_eq A] : ∀ s : finset A, clean s = s :=
take s, quot.induction_on s (λ l, eq.symm (quot.sound (eqv_norep l)))
theorem eq_of_clean_eq_clean {A : Type} [H : decidable_eq A] : ∀ s₁ s₂, clean s₁ = clean s₂ → s₁ = s₂ :=
take s₁ s₂, by rewrite *eq_clean; intro H; apply H
example : to_finset [(1:nat), 1, 2, 3] = to_finset [1, 2, 2, 2, 3, 3] :=
!eq_of_clean_eq_clean rfl
end finset