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Proof step 27 from proof band-011x-neg-03 (previous step)

0 ≤ i, 0 < j, i + 1 < j, abs(1 - j) ≤ i ⊦ (1 - j) % (i + 1) = (i + 2 - j) % (i + 1), j = 1, false ∈ int2bits(i).rest

User applied rule insert rewrite lemma

And obtained the following new goals

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 ≤ j + i0;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ 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