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Proof step 7 from proof perm-switch (previous step)

m < # y, n < # 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 = []

User applied rule case distinction

And obtained the following new goals

Proof step 8:
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)
Proof step 10:
n < # y, m < # y, ∀ a. a ∈ x ∨ a ∈ y → #oc(a, x) = #oc(a, y) ⊦ y = [], ∀ a. a ∈ x ∨ a ∈ y[m, y[n]][n, y[m]] → #oc(a, x) = #oc(a, y[m, y[n]][n, y[m]])

Rule argument

pos: right 1

Proof step 7 from proof perm-switch (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information