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Proof step 2 from proof product-del1-02 (previous step)

i ∈ ints ⊦ i * Π(ints -1l i) = Π ints

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ i. i ∈ ints0 → i * Π(ints0 -1l i) = Π ints0, i ∈ i0 + ints0 ⊦ i * Π((i0 + ints0) -1l i) = Π(i0 + ints0)

Rule argument

indvar: ints

Additional information

Used simplifier rules: prod-empty: ⊦ Π [] = 1;%intlist freely generated by [], +;;%del1-e: ⊦ [] -1l i = []; 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%in-empty: ⊦ ¬ i ∈ []; from specification list[intlista]