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Proof step 16 from proof product-all-elems-le (previous step)

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

User applied rule all left

And obtained the following new goals

Proof step 17:
i0 * i0 ^ n→i(# ints0) < i * Π ints0, i ≤ i0, 0 < i, 0 < i0, 0 ≤ i, 0 ≤ i0, i0 ^ n→i(# ints0) < Π ints0, 0 ≤ Π ints0, ∀ i1. i1 ∈ ints0 → 0 < i1 ∧ i1 ≤ i0, ¬ i0 ^ n→i(# ints0) < Π ints0 ∨ (∃ i. ¬(i ∈ ints0 → 0 < i ∧ i ≤ i0)) ⊦

Rule argument

pos: left 10 terms: i0 abort: F discard: T computed: T

Additional information

Used terms: i0