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Proof step 2 from proof del-05 (previous step)

perm(x, x -1l a), perm(x -1l a, x), a ∈ x ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ perm(x, y) ↔ (∀ a. a ∈ x ∨ a ∈ y → #oc(a, x) = #oc(a, y))
Proof step 4:
perm(x -1l a, x), a ∈ x, ∀ a0. a0 ∈ x ∨ a0 ∈ x -1l a → #oc(a0, x) = #oc(a0, x -1l a) ⊦

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] → [x -1l a, x] flags: <all paths>

Additional information

Used terms: x -1l a, x