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Proof step 2 from proof modeqp-neg (previous step)

i * i0 + j0 = i1 * j + j1, i + 1 < j + j0, i + 1 < j + j1, 0 ≤ i0, j0 < 0, j0 < j + j1, j0 + 1 < j + j1, 0 < j + j0, j1 < 0, j1 < j + j0, j1 + 1 < j + j0, 0 < j + j1, 0 ≤ j, i1 < 0, i1 < ~1, i0 ≤ j, i1 < i, i < 0, i < j + j0, i < j + j1, j0 + 1 < j, j1 + 1 < j, 0 < j, 1 < j, i1 < j + j0, i1 < j + j1, i + 1 < j ⊦

User applied rule insert 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] → [~ i, i0, ~ j0, ~ i1, j, ~ j1] flags: current, []

Additional information

Used simplifier rules: minus-left: ⊦ ~ i * j = ~(i * j);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%neg-11: ⊦ ~ 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%neg-12: ⊦ ~ i = ~ j ↔ i = j; from specification int-abs%negle-07: ⊦ i ≤ ~ j ↔ i + j ≤ 0; from specification int-abs%add-zero-rev: ⊦ 0 + i = i; from specification int-basic2%zero-gels-03: ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%neg-13: ⊦ ~ i < j ↔ 0 < j + i; from specification int-abs%neg-01: ⊦ ~ j < ~ i ↔ i < j; from specification int-abs Used terms: ~ i, i0, ~ j0, ~ i1, j, ~ j1