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Proof step 1 from proof modlsp-01 (conclusion)

j * i < j * i0 + j0, abs(j0) < j ⊦ i ≤ i0

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: modlsp seq: j * i < j * i0 + j0, 0 ≤ j0, j0 < j ⊦ i ≤ i0 subst: [j, i, i0, j0] → [j, i, i0, abs(j0)] flags: current, []

Additional information

Used simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%abs-03: ⊦ 0 ≤ abs(i); from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%ls-01: ⊦ i + j < i + i0 ↔ j < i0; from specification int-basic2%absls-01: ⊦ ¬ abs(i) < i; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: j, i, i0, abs(j0)