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Proof step 2 from proof modzero (previous step)

i * j + j0 < i, i * j + j0 < 0, abs(j0) < j, 0 < i, (i * j + j0) + 1 < i ⊦

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: modlsp-02 seq: j * i + j0 < j * i0, abs(j0) < j ⊦ i ≤ i0 subst: [j, i, j0, i0] → [j, i, j0, 0] flags: current, []

Additional information

Used simplifier rules: zero-left: ⊦ 0 * i = 0;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs Used terms: j, i, j0, 0