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Proof step 14 from proof modmod-add (previous step)

i0 + j0 = i3 * j + j2, j0 + i0 = i2 * j + j1, 0 ≤ j2, j2 < j, 0 ≤ i1 * j + i0 + j0, 0 ≤ i0 + j0, 0 ≤ j1, j1 < j, 0 ≤ j0 + i0, 0 ≤ i0, 0 ≤ j0, j0 < j, 0 ≤ i1, 0 < j ⊦ j1 = j2

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: modeqp seq: i * j + j0 = i0 * j + j1, 0 ≤ j0, j0 < j, 0 ≤ j1, j1 < j ⊦ i = i0 ∧ j0 = j1 subst: [i, j, j0, i0, j1] → [i2, j, j1, i3, j2] flags: []

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs Used terms: i2, j, j1, i3, j2