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Proof step 21 from proof modmod-pos (previous step)

j2 < j0, j1 < j, 0 < j, 0 ≤ j1, 0 ≤ j2, 0 ≤ i1, 0 < j0, j * j0 < j2 * j + j1 ⊦ j * j0 = j2 * j + j1, (j2 * j + j1) % (j * j0) = j1 + j2 * j

User applied rule insert spec-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, j0, j2, j1] flags:

Additional information

Used simplifier rules: lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j, j0, j2, j1