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Proof step 5 from proof del-04 (previous step)

perm(x, y), perm(y, x), a0 ∈ x -1l a ∨ a0 ∈ y -1l a ⊦ #oc(a0, x -1l a) = #oc(a0, y -1l a)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ perm(x, y) ↔ (∀ a. a ∈ x ∨ a ∈ y → #oc(a, x) = #oc(a, y))
Proof step 7:
∀ a. a ∈ x ∨ a ∈ y → #oc(a, x) = #oc(a, y), perm(y, x), a0 ∈ x -1l a ∨ a0 ∈ y -1l a ⊦ #oc(a0, x -1l a) = #oc(a0, y -1l a)

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, x] flags: rewrite, current

Additional information

Used terms: y, x