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Proof step 1 from proof del-02 (conclusion)

⊦ perm(x -1l a, y -1l a) ∧ a ∈ x ∧ a ∈ y → perm(x, y)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
a ∈ x, a ∈ y, ∀ a0. #oc(a0, x -1l a) ≤ #oc(a0, y -1l a), ∀ a0. #oc(a0, y -1l a) ≤ #oc(a0, x -1l a) ⊦ #oc(a0, x) ≤ #oc(a0, y) ∧ #oc(a1, y) ≤ #oc(a1, 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));