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Proof step 22 from proof band-011x-neg-03 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ i + j = j + i
Proof step 24:
0 ≤ i, 0 < j, i + 1 < j ⊦ (1 - j) % (i + 1) = ((i + 1) + (1 - j)) % (i + 1), false ∈ int2bits(i).rest

Rule argument

seq: ⊦ i + j = j + i subst: [j, i] → [i + 1, 1 - j] rotate: F spec: int-basic2 inst: name: add-c

Additional information

Used terms: i + 1, 1 - j