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Proof step 3 from proof modzero (previous step)

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

Additional information

Used simplifier rules: zero-left: ⊦ 0 * i = 0;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;% ⊦ i < j → (j ≤ i ↔ false); (as)% ⊦ i < j ↔ ¬ j ≤ i; (ss) Used terms: j, i, j0, 0