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Proof step 14 from proof perm-del-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ perm(x, y) ↔ (∀ a. a ∈ x ∨ a ∈ y → #oc(a, x) = #oc(a, y))
Proof step 16:
perm(x -l a, z), perm(x, y), ∀ a0. a0 ∈ z ∨ a0 ∈ x -l a → #oc(a0, z) = #oc(a0, x -l a), a0 ∈ y ∨ a0 ∈ x → #oc(a0, y) = #oc(a0, x), a0 ∈ y ∨ a0 ∈ z ⊦ #oc(a0, y) = #oc(a0, z), a0 = 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] → [x -l a, z] flags: rewrite, current

Additional information

Used terms: x -l a, z