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Proof step 2 from proof product-pot-rec (previous step)

i ∈ ints ⊦ Π ints = i ^ n→i(#oc(i, ints)) * Π(ints -l i)

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ i. i ∈ ints0 → Π ints0 = i ^ n→i(#oc(i, ints0)) * Π(ints0 -l i), i ∈ i0 + ints0 ⊦ Π(i0 + ints0) = i ^ n→i(#oc(i, i0 + ints0)) * Π((i0 + ints0) -l i)

Rule argument

indvar: ints

Additional information

Used simplifier rules: intlist freely generated by [], +;;%prod-empty: ⊦ Π [] = 1; from specification intlist%oc-e: ⊦ #oc(i, []) = 0; from specification list-perm[intlista]%Pot-zero: ⊦ j ^ 0 = 1; from specification int-pot%del-e: ⊦ [] -l i = []; from specification list-del[intlista]%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult