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Proof step 2 from proof perm-put-del1 (previous step)

n < # y ⊦ y = [], perm(y[n, a] -1l a, y -1l y[n])

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:
n < # y ⊦ y = [], ∀ a0. a0 ∈ y[n, a] -1l a ∨ a0 ∈ y -1l y[n] → #oc(a0, y[n, a] -1l a) = #oc(a0, y -1l y[n])

Rule argument

spec: inst: name: perm-all seq: ⊦ perm(x, y) ↔ (∀ a. a ∈ x ∨ a ∈ y → #oc(a, x) = #oc(a, y)) subst: [y, x] → [y -1l y[n], y[n, a] -1l a] flags: rewrite, current

Additional information

Used terms: y -1l y[n], y[n, a] -1l a