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Proof step 10 from proof mod-pred-neg (previous step)

i0 * j + j0 = (i2 * j + j1) + 1, abs(j1) < j, i0 < j, i0 ≤ 0, j0 < j, j0 ≤ 0, 0 < j, abs(j0) < j, i2 * j + j1 < ~1, j1 ≤ 0, j1 < j, i2 ≤ 0, i2 < j, i2 * j + j1 < 0 ⊦ 1 = j0 + j, j0 = j1 + 1

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 11:
i * j + j0 = i0 * j + j1, 0 ≤ j0, j0 < j, 0 ≤ j1, j1 < j ⊦ i = i0 ∧ j0 = j1
Proof step 12:
i0 * j + j0 = (i2 * j + j1) + 1, abs(j1) < j, i0 < j, i0 ≤ 0, j0 < j, j0 ≤ 0, 0 < j, abs(j0) < j, i2 * j + j1 < ~1, j1 ≤ 0, j1 < j, i2 ≤ 0, i2 < j, i2 * j + j1 < 0 ⊦ i0 * j + ~(j1 + 1) = i2 * j + ~ j0 ∧ 0 ≤ ~(j1 + 1) ∧ ~(j1 + 1) < j ∧ 0 ≤ ~ j0 ∧ ~ j0 < j, 1 = j0 + j, j0 = j1 + 1

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 + 1), i2, ~ j0] flags: []

Additional information

Used simplifier rules: neg-12: ⊦ ~ i = ~ j ↔ i = j; from specification int-abs Used terms: i0, j, ~(j1 + 1), i2, ~ j0