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Proof step 20 from proof abs-ls-same-01 (previous step)

j < 0, i ≤ abs(i) * j ⊦ j = ~1, i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ i < 0 → abs((* i)) = ~ i
Proof step 22:
i < 0, j < 0, i ≤ ~ i * j ⊦ j = ~1, i = 0

Rule argument

spec: int-abs inst: name: numabsneg seq: ⊦ i < 0 → abs((* i)) = ~ i subst: [i] → [i] flags: rewrite

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;%lst-01: ⊦ ¬ i < j → (i ≠ j ↔ j < i); from specification int-basic1%abs-16: ⊦ 0 < j → abs(j) = j; from specification int-abs%leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: i