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Proof step 11 from proof div-ls (previous step)

0 < j, 0 < j0, 0 < j1, i0 * j + j2 < j1 * j, j2 < j, j1 < i0, 1 < i0, 0 < i0, j0 ≤ i0, j1 ≤ j0, 0 ≤ j2, 0 ≤ i0 ⊦ i0 = j1, j = 0

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: int-mult name: modlsp-02 seq: j * i + j0 < j * i0, abs(j0) < j ⊦ i ≤ i0 subst: [j, i, j0, i0] → [j, i0, j2, j1]

Additional information

Used simplifier rules: ⊦ i ≠ j → (i ≤ j ↔ i < j); (s)% ⊦ i < j → ¬ j < i; (s)%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ 0 ≤ i → abs(i) = i; (s) Used terms: j, i0, j2, j1