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Proof step 8 from proof div-est-denom-pos (previous step)

i1 * j + j1 = i2 * j0 + j2, j2 < j0, j1 < j, i0 ≤ i2, j ≤ j0, i1 < i0, 0 < j0, 0 < j, 0 ≤ j1, j1 < j0, 0 ≤ i1, 0 < i0, 0 ≤ j2, 0 ≤ i2, i1 < i2, 0 < i2 ⊦

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: modneqp seq: i * i0 + j0 = i1 * j + j1, 0 ≤ j1, j1 < j, 0 ≤ j0, j0 < j, 0 ≤ i0, i0 ≤ j, 0 ≤ i, i < i1 ⊦ subst: [i, i0, j0, i1, j, j1] → [i1, j, j1, i2, j0, j2] flags: []

Additional information

Used simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: i1, j, j1, i2, j0, j2