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Proof step 2 from proof trans (previous step)

∀ 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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ perm(x, y) ↔ x ⊆m y ∧ y ⊆m x
Proof step 4:
∀ 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) ⊦ x ⊆m z ∧ z ⊆m x

Rule argument

spec: list-perm inst: name: perm seq: ⊦ perm(x, y) ↔ x ⊆m y ∧ y ⊆m x subst: [y, x] → [z, x] flags: rewrite, current

Additional information

Used terms: z, x