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Proof step 3 from proof perm-del-01 (previous step)

perm(x, y), perm(x -l a, z), perm(y, x), perm(z, x -l a) ⊦ perm(y -l a, z)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ perm(x, y) ↔ (∀ a. a ∈ x ∨ a ∈ y → #oc(a, x) = #oc(a, y))
Proof step 5:
perm(z, x -l a), perm(y, x), perm(x -l a, z), perm(x, y) ⊦ ∀ a0. a0 ∈ y -l a ∨ a0 ∈ z → #oc(a0, y -l a) = #oc(a0, z)

Rule argument

spec: <toplevel> name: perm-all seq: ⊦ perm(x, y) ↔ (∀ a. a ∈ x ∨ a ∈ y → #oc(a, x) = #oc(a, y)) subst: [y, x] → [z, y -l a] flags: <all paths>

Additional information

Used terms: z, y -l a