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Proof step 11 from proof band-011x-neg-03 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: 0 < j, j ≤ i ⊦ i % j = (i - j) % j subst: [j, i] → [i + 1, i + 1 - j] rotate: F spec: int-div inst: name: mod-rec

Additional information

Used simplifier rules: ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i - j - i0 = i - j + i0;% ⊦ i + j - i0 + j = i - i0;% ⊦ i - j + i = ~ j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ i < 1 ↔ i ≤ 0;% ⊦ i + j < i + i0 ↔ j < i0;% ⊦ i < j - i0 ↔ i + i0 < j;% ⊦ i + 1 ≤ j ↔ i < j;% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0;%j ≠ 0 ⊦ ~ i % j = ~(i % j);% ⊦ ~ i + i = 0; Used terms: i + 1, i + 1 - j