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Proof step 36 from proof band-011x-neg-03 (previous step)

i < abs(1 - j), 0 < j, j ≤ i + 1, 0 ≤ i ⊦ 1 = (1 - j) % (i + 1) + j, 1 = j, false ∈ int2bits(i).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ j < 0 → abs(j) = 0 - j

Rule argument

seq: ⊦ j < 0 → abs(j) = 0 - j subst: [j] → [1 - j] rotate: F spec: int-abs inst: name: Abs-neg

Additional information

Used simplifier rules: ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ~(i - j) = j - i;% ⊦ 0 - i = ~ i;% ⊦ ¬ j < 0 → abs(j) = j;% ⊦ i < j - i0 ↔ i + i0 < j;% ⊦ i < 1 ↔ i ≤ 0;% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ i + 0 = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 < i → (i ≤ 1 ↔ i = 1); Used terms: 1 - j