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Proof step 21 from proof divides-prime (previous step)

2 ≤ i0 * i, i < 0, i0 < 0, ∀ i1. 1 < i1 ∧ i1 < i0 * i → ¬ i1 | i0 * i, 1 < ~ i0 ∧ ~ i0 < i0 * i → ¬ i0 | i * i0 ⊦ i0 = 0, ~1 = i, i = 0, ~1 = i0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
2 ≤ i0 * i, i < 0, i0 < 0, ∀ i1. 1 < i1 ∧ i1 < i0 * i → ¬ i1 | i0 * i ⊦ i0 = 0, ~1 = i, i = 0, ~1 = i0, 1 < ~ i0 ∧ ~ i0 < i0 * i

Rule argument

Additional information

Used simplifier rules: div-mult: ⊦ i | i * j;%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult