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Proof step 1 from proof trans (conclusion)

⊦ perm(x, y) ∧ perm(y, z) → perm(x, z)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
∀ a. #oc(a, z) ≤ #oc(a, y), ∀ a. #oc(a, y) ≤ #oc(a, z), ∀ a. #oc(a, y) ≤ #oc(a, x), ∀ a. #oc(a, x) ≤ #oc(a, y) ⊦ perm(x, z)

Rule argument

Additional information

Used simplifier rules: perm: ⊦ perm(x, y) ↔ x ⊆m y ∧ y ⊆m x;%msubset: ⊦ x ⊆m y ↔ (∀ a. #oc(a, x) ≤ #oc(a, y));%sym-02: ⊦ ¬ perm(x, y) → ¬ perm(y, x);%sym-02: ⊦ ¬ perm(x, y) → ¬ perm(y, x);