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Proof step 17 from proof mod-neg (previous step)

i0 * j + j0 = i1 * j + j1, abs(j1) < j, 0 < j, i0 ≤ 0, i0 < j, i0 < j + j0, j0 < 0, j0 < j, 0 < j + j0, i1 ≤ 0, i1 < j, i1 < j + j0, j1 ≤ 0, j1 < j, j1 < j + j0, i1 * j + j1 < 0, i1 * j + j1 < j, i1 * j + j1 < j + j0 ⊦ j0 = j1

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] → [i0, j, ~ j1, i1, ~ j0] flags: []

Additional information

Used simplifier rules: neg-12: ⊦ ~ i = ~ j ↔ i = j; from specification int-abs%neg-15: ⊦ i + ~ j = i - j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs%sub-add-01: ⊦ i + (j - i0) = i + j - i0; from specification int-abs%negle-07: ⊦ i ≤ ~ j ↔ i + j ≤ 0; from specification int-abs%ax-04: ⊦ i + 0 = i; from specification int-basic2%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%neg-13: ⊦ ~ i < j ↔ 0 < j + i; from specification int-abs%zero-gels-03: ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%ls-01: ⊦ i + j < i + i0 ↔ j < i0; from specification int-basic2%ls: ⊦ i + j < j ↔ i < 0; from specification int-basic2%abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs Used terms: i0, j, ~ j1, i1, ~ j0