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Proof step 6 from proof mods-ls-04 (previous step)

j0 < j, 0 < j, i * j + j0 < i0 * j, 0 ≤ j0, 0 ≤ i0, i0 ≤ i, 0 ≤ i ⊦

User applied rule apply lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i;% ⊦ i ≤ j → (j ≤ i ↔ i = j); (s)% ⊦ i + j < j ↔ i < 0; (s)% ⊦ i ≤ j → (j < i ↔ false); (as)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ 0 ≤ i → abs(i) = i; (s) Used terms: j, i, j0, i0