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Proof step 8 from proof modeqp-03 (previous step)

i * j + j0 = i0 * j + j1, j1 < 0, j < j1, j < j0, j < 0, j1 ≤ 0, j0 ≤ 0 ⊦ i = i0 ∧ j0 = j1, j - j1 < 0 ∧ abs(j0) + j < 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ j < 0 → abs(j) = 0 - j

Rule argument

spec: int-abs name: Abs-neg seq: ⊦ j < 0 → abs(j) = 0 - j subst: [j] → [j0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 0 - i = ~ i; (s)% ⊦ i + ~ j = i - j; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; (s)% ⊦ i + 0 = i; (s)% ⊦ i < j → (j ≤ i ↔ false); (as)% ⊦ i ≤ j → (j ≤ i ↔ i = j); (s) Used terms: j0