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Proof step 8 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]]) ⊦ y = [], ∀ a. a ∈ x ∨ a ∈ y → #oc(a, x) = #oc(a, y)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
m < # y, n < # y, ∀ a0. a0 ∈ x ∨ a0 ∈ y → #oc(a0, x) = #oc(a0, y), a ∈ x ∨ a ∈ y ⊦ #oc(a, x) = #oc(a, y), y = []

Rule argument

Additional information

Used simplifier rules: ocs-sw: ⊦ m < # x ∧ n < # x → #oc(a, x[m, x[n]][n, x[m]]) = #oc(a, x);% ⊦ m < # x ∧ n < # x → (a ∈ x[m, x[n]][n, x[m]] ↔ a ∈ x); (s)