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Proof step 8 from proof gcd-prime (previous step)

i0 | i, i0 | j, 1 < i, 2 < j, 0 < i, i < j, 2 ≤ j, 0 < j, 0 < i0, 1 < i0, 0 ≤ j, ∀ i. 1 < i ∧ i < j → ¬ i | j ⊦

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 12 terms: i0

Additional information

Used simplifier rules: div-not-ls: ⊦ i < j ∧ 0 < i → ¬ j | i;%numlelsdel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < j; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%numlsledel-01: i0 ≠ 0, i0 < i ⊦ (* i) ≤ j → (* i0) < j; from specification int-abs Used terms: i0