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Proof step 4 from proof perm-switch (previous step)

n < # y, m < # y ⊦ (∀ a. a ∈ x ∨ a ∈ y[m, y[n]][n, y[m]] → #oc(a, x) = #oc(a, y[m, y[n]][n, y[m]])) ↔ perm(x, y), y = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ perm(x, y) ↔ (∀ a. a ∈ x ∨ a ∈ y → #oc(a, x) = #oc(a, y))
Proof step 6:
n < # y, m < # y ⊦ (∀ a. a ∈ x ∨ a ∈ y[m, y[n]][n, y[m]] → #oc(a, x) = #oc(a, y[m, y[n]][n, y[m]])) ↔ (∀ a. a ∈ x ∨ a ∈ y → #oc(a, x) = #oc(a, y)), y = []

Rule argument

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

Additional information

Used terms: y, x