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Proof step 4 from proof product-divide (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ perm(i ' + ints, ints0) ↔ ¬ ¬(i ∈ ints0 ∧ perm(ints, ints0 -1l i))
Proof step 6:
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

Rule argument

spec: list-perm inst: intlista name: del-01 seq: ⊦ perm(i ' + ints, ints0) ↔ ¬ ¬(i ∈ ints0 ∧ perm(ints, ints0 -1l i)) subst: [ints0, ints, i] → [ints0 + ints1, ints2, i] flags: rewrite

Additional information

Used terms: ints0 + ints1, ints2, i