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Proof step 11 from proof perm-all (previous step)

a ∈ x ∨ a ∈ y → #oc(a, x) = #oc(a, y), ∀ a. a ∈ x ∨ a ∈ y → #oc(a, x) = #oc(a, y) ⊦ #oc(a, x) ≤ #oc(a, y) ∧ #oc(a0, y) ≤ #oc(a0, x)

User applied rule cut formula

And obtained the following new goals

Proof step 12:
a ∈ x ∨ a ∈ y, a ∈ x ∨ a ∈ y → #oc(a, x) = #oc(a, y), ∀ a. a ∈ x ∨ a ∈ y → #oc(a, x) = #oc(a, y) ⊦ #oc(a, x) ≤ #oc(a, y) ∧ #oc(a0, y) ≤ #oc(a0, x)
Proof step 14:
a ∈ x ∨ a ∈ y → #oc(a, x) = #oc(a, y), ∀ a. a ∈ x ∨ a ∈ y → #oc(a, x) = #oc(a, y) ⊦ a ∈ x ∨ a ∈ y, #oc(a, x) ≤ #oc(a, y) ∧ #oc(a0, y) ≤ #oc(a0, x)

Rule argument

fma: a ∈ x ∨ a ∈ y

Additional information

Used formulas: a ∈ x ∨ a ∈ y