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Proof step 1 from proof product-app (conclusion)

⊦ Π(ints + ints0) = Π ints * Π ints0

User applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ ints0. Π(ints1 + ints0) = Π ints1 * Π ints0 ⊦ Π((i + ints1) + ints0) = Π(i + ints1) * Π ints0

Rule argument

indvar: ints

Additional information

Used simplifier rules: prod-empty: ⊦ Π [] = 1;%intlist freely generated by [], +;;%Nil: ⊦ [] + ints = ints; from specification list[intlista]%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[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