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Proof step 17 from proof perm-del-01 (previous step)

perm(x -l a, z), perm(x, y), 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
perm(x -l a, z), perm(x, y), a0 ∈ y ∨ a0 ∈ x → #oc(a0, y) = #oc(a0, x), a0 ∈ y ∨ a0 ∈ z, a0 ∈ z ∨ a0 ∈ x → #oc(a0, z) = #oc(a0, x) ⊦ #oc(a0, y) = #oc(a0, z), a0 = a

Rule argument

Additional information

Used simplifier rules: ocs-del-length: ⊦ a ≠ b → #oc(a, x -l b) = #oc(a, x);%in-del-new: ⊦ a ∈ x -l b ↔ a ∈ x ∧ a ≠ b; from specification list-del