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Proof step 7 from proof mod-nls-06 (previous step)

i0 < i % ~ j, j ≤ i0 + 1, ~1 ≤ j + i0, j < 0 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: mod-nls-05 seq: ⊦ j ≤ i0 + 1 ∧ 0 < j → ¬ i0 < i % j subst: [j, i, i0] → [~ j, i, i0] flags: rewrite, current

Additional information

Used simplifier rules: mod-neg: j ≠ 0 ⊦ i % ~ j = i % j;%numle-02: ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0; 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%add-zero-rev: ⊦ 0 + i = i; from specification int-basic2%negle-13: ⊦ ~ i ≤ j ↔ 0 ≤ i + j; from specification int-abs%numleledel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j; from specification int-abs%neg: ⊦ 0 < ~ i ↔ i < 0; from specification int-abs%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs Used terms: ~ j, i, i0