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Proof step 16 from proof divides-prime (previous step)

¬ 0 < i0, 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%numleledel: j0 ≠ 0, j ≤ j0 ⊦ i ≤ (* j) → i ≤ (* j0); from specification int-abs%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%lsone: ⊦ i < 1 ↔ i ≤ 0; from specification int-abs%ls-same-03: ⊦ i < 0 → (i < i * j ↔ j < 1); from specification int-mult%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%zero-ge-01: ⊦ i < 0 → (0 ≤ i * j ↔ j ≤ 0); from specification int-mult%zero-eq: ⊦ i * j = 0 ↔ i = 0 ∨ j = 0; from specification int-mult%succ-rmerge: ⊦ i * j + i = i * (j + 1); from specification int-mult%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%numadd-01: ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0; from specification int-abs%negeq: ⊦ ~ i = j ↔ i + j = 0; from specification int-abs%abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%zero-gr-03: ⊦ i ≤ 0 → (0 < i * j ↔ ¬ ¬(j < 0 ∧ i ≠ 0)); from specification int-mult%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs