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Proof step 14 from proof divides-prime (previous step)

0 < i0 * i, 0 ≤ i0 * i, 2 ≤ i0 * i, i0 < i0 * i, i0 ≤ 1, ∀ 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 inst: name: ls-same-01 seq: ⊦ 0 < i → (i < i * j ↔ 1 < j) subst: [j, i] → [i, i0] flags: rewrite

Additional information

Used simplifier rules: abs: ⊦ 1 < i → abs(i) = i; from specification int-abs%eq-same: ⊦ i * j = i ↔ i = 0 ∨ j = 1; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%zero-ge: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); from specification int-mult%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%bet: ⊦ 0 < i → (i ≤ 1 ↔ i = 1); from specification int-abs Used terms: i, i0