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Proof step 3 from proof product-divide (previous step)

∀ ints0, ints1. perm(ints2, ints0 + ints1) → Π ints2 = Π ints0 * Π ints1, perm(i + ints2, ints0 + ints1) ⊦ Π(i + ints2) = Π ints0 * Π ints1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
perm(i ' + ints2, ints0 + ints1), ∀ ints0, ints1. perm(ints2, ints0 + ints1) → Π ints2 = Π ints0 * Π ints1 ⊦ i * Π ints2 = Π ints0 * Π ints1

Rule argument

Additional information

Used simplifier rules: product-app: ⊦ Π(ints + ints0) = Π ints * Π ints0;%product-one: ⊦ Π i ' = i;%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%c: ⊦ i + ints = i ' + ints; from specification list[intlista]