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Proof step 6 from proof div-add-nosucc-neg (previous step)

j ≠ 0, i % j = 0, i < j, 0 < j, 1 < j, i < 0, j + i ≤ 0, i + 1 < j ⊦ j = 1, ~((~ i + (j - 1)) / j) = i / j

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: div-add-nosucc seq: ⊦ 1 < j ∧ 0 ≤ i ∧ i % j = 0 → (i + (j - 1)) / j = i / j subst: [j, i] → [j, ~ i] flags: rewrite, current

Additional information

Used simplifier rules: mod-neg-01: j ≠ 0 ⊦ ~ i % j = ~(i % j);%mod-neg-01: j ≠ 0 ⊦ ~ i % j = ~(i % j);%Div-left: ⊦ j ≠ 0 → ~ i / j = ~(i / j);%neg-10: ⊦ ~ i = 0 ↔ i = 0; from specification int-abs%neg-02: ⊦ ~ ~ i = i; from specification int-abs%sub-add-01: ⊦ i + (j - i0) = i + j - i0; 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-sub: ⊦ i - j - i0 = i - j + i0; from specification int-abs%negeq: ⊦ ~ i = j ↔ i + j = 0; from specification int-abs%numlelsdel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < 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 Used terms: j, ~ i