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Proof step 15 from proof divides-prime (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult name: ls-same-01 seq: ⊦ 0 < i → (i < i * j ↔ 1 < j) subst: [j, i] → [i, i0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 1 < i → abs(i) = i; (s)% ⊦ i * j = i ↔ i = 0 ∨ j = 1; (ws)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ 0 < i → (i ≤ 1 ↔ i = 1); (s) Used terms: i, i0