Created
February 28, 2017 23:06
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constant heap : Type | |
constant ptr : Type | |
constant val : Type | |
constant pt : ptr → val → heap | |
constant hunion : heap → heap → heap | |
constant is_def : heap → Prop | |
infix `∙`:60 := hunion | |
infix `↣`:70 := pt | |
/- | |
constant hunion_is_assoc : is_associative heap hunion | |
constant hunion_is_comm : is_commutative heap hunion | |
attribute [instance] hunion_is_comm hunion_is_assoc | |
axiom noalias : ∀ (h : heap) (y₁ y₂ : ptr) (w₁ w₂ : val), is_def (h ∙ y₁ ↣ w₁ ∙ y₂ ↣ w₂) → y₁ ≠ y₂ | |
-/ | |
-- set_option profiler true | |
lemma ex | |
(h₁ h₂ h₃ h₄ : heap) (x₁ x₂ x₃ x₄ : ptr) (v₁ v₂ v₃ : val) | |
(hcomm : ∀ x y, x ∙ y = y ∙ x) | |
(hassoc : ∀ x y z, (x ∙ y) ∙ z = x ∙ (y ∙ z)) | |
(hnoalias : ∀ h y₁ y₂ w₁ w₂, is_def (h ∙ y₁ ↣ w₁ ∙ y₂ ↣ w₂) → y₁ ≠ y₂) | |
: is_def (h₁ ∙ h₃ ∙ (x₁ ↣ v₁ ∙ x₂ ↣ v₂) ∙ h₄ ∙ h₂ ∙ (x₃ ↣ v₃)) → x₁ ≠ x₃ ∧ x₁ ≠ x₂ ∧ x₂ ≠ x₃ := | |
begin [smt] with {em_cfg := {max_instances := 1000000, max_generation := 100}}, | |
intros, | |
smt_tactic.add_lemmas_from_facts, | |
repeat {ematch} | |
end |
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