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Proof step 3 from proof mod-mult-neg-01 (previous step)

⊦ 0 < j ∧ i ≤ 0 ∧ 0 ≤ i0 ∧ i0 < j → (j * i + ~ i0) % j = ~ i0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: mod-mult-neg seq: ⊦ 0 < j ∧ i ≤ 0 ∧ i0 ≤ 0 ∧ abs(i0) < j → (j * i + i0) % j = i0 subst: [i0, i, j] → [~ i0, i, j] flags: rewrite, current

Additional information

Used simplifier rules: 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%negeq: ⊦ ~ i = j ↔ i + j = 0; from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%negle-13: ⊦ ~ i ≤ j ↔ 0 ≤ i + j; from specification int-abs%add-zero-rev: ⊦ 0 + i = i; from specification int-basic2%abs-neg: ⊦ abs(~ i) = abs(i); from specification int-abs%absle: ⊦ 0 ≤ i → abs(i) = i; from specification int-abs Used terms: ~ i0, i, j