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Proof step 1 from proof shift-02 (conclusion)

⊦ perm(x + x0, y) ↔ perm(x0 + x, y)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ (∀ a. #oc(a, x) + #oc(a, x0) ≤ #oc(a, y)) ∧ (∀ a. #oc(a, y) ≤ #oc(a, x) + #oc(a, x0)) ↔ (∀ a. #oc(a, x0) + #oc(a, x) ≤ #oc(a, y)) ∧ (∀ a. #oc(a, y) ≤ #oc(a, x0) + #oc(a, x))

Rule argument

Additional information

Used simplifier rules: perm-def: ⊦ perm(x, y) ↔ ¬ ¬(x ⊆m y ∧ y ⊆m x);%msubset: ⊦ x ⊆m y ↔ (∀ a. #oc(a, x) ≤ #oc(a, y));%ocappend: ⊦ #oc(a, x + y) = #oc(a, x) + #oc(a, y);%a: ⊦ (x + y) + z = x + y + z; from specification list