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Proof step 1 from proof modeqp-01 (conclusion)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 2:
i * j + j0 = i0 * j + j1, 0 ≤ j0, j0 < j, 0 ≤ j1, j1 < j ⊦ i = i0 ∧ j0 = j1
Proof step 3:
i * j + j0 = i0 * j + j1, j0 ≤ 0, abs(j0) < j, j1 ≤ 0, abs(j1) < j ⊦ i * j + ~ j1 = i0 * j + ~ j0 ∧ 0 ≤ ~ j1 ∧ ~ j1 < j ∧ 0 ≤ ~ j0 ∧ ~ j0 < j, i = i0 ∧ j0 = j1

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] → [i, j, ~ j1, i0, ~ j0] flags: current, []

Additional information

Used simplifier rules: neg-12: ⊦ ~ i = ~ j ↔ i = j; from specification int-abs%add-in: ⊦ i + j = i + i0 ↔ j = i0; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: i, j, ~ j1, i0, ~ j0