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Proof step 2 from proof product-zero (previous step)

0 ∈ ints ⊦ Π ints = 0

User applied rule structural induction

And closed the goal!

Rule argument

indvar: ints

Additional information

Used simplifier rules: prod-empty: ⊦ Π [] = 1;%product-app: ⊦ Π(ints + ints0) = Π ints * Π ints0;%product-one: ⊦ Π i ' = i;%intlist freely generated by [], +;;%c: ⊦ i + ints = i ' + ints; from specification list[intlista]%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%zero-eq: ⊦ i * j = 0 ↔ i = 0 ∨ j = 0; 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-01: ⊦ i ≠ i0 → (i ∈ i0 ' + ints ↔ i ∈ ints); from specification list[intlista]%in-empty: ⊦ ¬ i ∈ []; from specification list[intlista]