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Proof step 5 from proof prime-mult-not (previous step)

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

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 7 terms: i

Additional information

Used simplifier rules: div-mult: ⊦ i | i * j;%ls-same-01: ⊦ 0 < i → (i < i * j ↔ 1 < j); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i