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Proof step 23 from proof product-all-elems-le (previous step)

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

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 10 terms: i1

Additional information

Used simplifier rules: ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: i1