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Proof step 9 from proof product-pot-rec (previous step)

∀ i. i ∈ ints0 → Π ints0 = i ^ n→i(#oc(i, ints0)) * Π(ints0 -l i) ⊦ i0 = 0, Π ints0 = i0 ^ n→i(#oc(i0, ints0)) * Π(ints0 -l i0)

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 1 terms: i0

Additional information

Used simplifier rules: notin: ⊦ ¬ i ∈ ints → #oc(i, ints) = 0; from specification list-perm[intlista]%Pot-zero: ⊦ j ^ 0 = 1; from specification int-pot%in-03: ⊦ ¬ i ∈ ints → ints -l i = ints; from specification list-del[intlista]%one: ⊦ 1 * i = i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i0