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Proof step 4 from proof oc-filt (previous step)

a ∈ y, ∀ a, y. a ∈ y → #oc(a, filter(x0, y)) = #oc(a, x0) ⊦ #oc(a, filter(a0 ' + x0, y)) = #oc(a, a0 ') + #oc(a, x0)

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 5:
a0 = a, a ∈ y, ∀ a, y. a ∈ y → #oc(a, filter(x0, y)) = #oc(a, x0) ⊦ #oc(a, filter(a0 ' + x0, y)) = #oc(a, a0 ') + #oc(a, x0)
Proof step 7:
a ∈ y, ∀ a, y. a ∈ y → #oc(a, filter(x0, y)) = #oc(a, x0) ⊦ a0 = a, #oc(a, filter(a0 ' + x0, y)) = #oc(a, a0 ') + #oc(a, x0)

Rule argument

fma: a0 = a

Additional information

Used formulas: a0 = a