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Proof step 15 from proof product-all-elems-le (previous step)

0 ≤ Π ints0, i0 * i0 ^ n→i(# ints0) < i * Π ints0, i ≤ i0, 0 < i, 0 < i0, 0 ≤ i, 0 ≤ i0, ∀ i1. i1 ∈ ints0 → 0 < i1 ∧ i1 ≤ i0, ∀ i1. ¬ i1 ^ n→i(# ints0) < Π ints0 ∨ (∃ i. ¬(i ∈ ints0 → 0 < i ∧ i ≤ i1)) ⊦ 0 ≤ Π ints0 ∧ Π ints0 ≤ i0 ^ n→i(# ints0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs