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Proof step 19 from proof bint-mod (previous step)

2147483648 < abs(j), j < i % j, 0 < i % j, j ≤ 2147483647, ~2147483648 ≤ j, 2147483647 < i % j ⊦ j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs inst: name: Abs-neg seq: ⊦ j < 0 → abs(j) = 0 - j subst: [j] → [j] flags: rewrite

Additional information

Used simplifier rules: mod-nls-05: ⊦ j ≤ i0 + 1 ∧ 0 < j → ¬ i0 < i % j; from specification int-div%Abs-pos: ⊦ ¬ j < 0 → abs(j) = j; from specification int-abs%lst-01: ⊦ ¬ i < j → (i ≠ j ↔ j < i); from specification int-basic1%neg-06: ⊦ 0 - i = ~ i; from specification int-abs%neg-07: ⊦ i < ~ j ↔ i + j < 0; from specification int-abs%numls-03: ⊦ i + (* j) < (* j0) ↔ i < j0 - j; from specification int-abs%lels-04: ⊦ i ≤ j → (¬ ¬ j < i ↔ false); 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 Used terms: j