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Proof step 22 from proof abs-ls-same-01 (previous step)

j < 0, i ≤ abs(i) * j ⊦ i = 0, j = ~1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ j < 0 → abs(j) = 0 - j
Proof step 24:
j < 0, i < 0, i ≤ (0 - i) * j ⊦ i = 0, j = ~1

Rule argument

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

Additional information

Used simplifier rules: le-same-01: ⊦ 0 < i → (i ≤ i * j ↔ 1 ≤ j);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;% ⊦ ¬ i < j → (i = j ↔ ¬ j < i); (ss)% ⊦ ¬ j < 0 → abs(j) = j; (s)% ⊦ 1 ≤ i ↔ 0 < i; (s)% ⊦ i < j → ¬ j < i; (s) Used terms: i