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Proof step 6 from proof product-divide (previous step)

i ∈ ints0 + ints1 ∧ perm(ints2, (ints0 + ints1) -1l i), ∀ ints0, ints1. perm(ints2, ints0 + ints1) → Π ints2 = Π ints0 * Π ints1 ⊦ i * Π ints2 = Π ints0 * Π ints1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
perm(ints2, (ints0 + ints1) -1l i), ∀ ints0, ints1. perm(ints2, ints0 + ints1) → Π ints2 = Π ints0 * Π ints1 ⊦ i * Π ints2 = Π ints0 * Π ints1, ¬ i ∈ ints0 ∧ ¬ i ∈ ints1

Rule argument

Additional information

Used simplifier rules: a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%in-append: ⊦ i ∈ ints + ints0 ↔ ¬ ¬(i ∈ ints ∨ i ∈ ints0); from specification list[intlista]