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Proof step 33 from proof band-011x-neg-03 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
⊦ abs(i) < j → i % j = i
Proof step 35:
¬ abs(1 - j) < i + 1, 0 ≤ i, j ≤ i + 1, 0 < j ⊦ 1 = (1 - j) % (i + 1) + j, false ∈ int2bits(i).rest

Rule argument

seq: ⊦ abs(i) < j → i % j = i subst: [j, i] → [i + 1, 1 - j] rotate: F spec: int-div inst: name: mod-zero-05

Additional information

Used simplifier rules: ⊦ i + (j - i) = j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: i + 1, 1 - j