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Proof step 244 from proof int2bytes-rec-neg-05 (previous step)

# (mklist(false, i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))).rest % 8 = 0, # int2bits(j % 2 ^ (i * 8)) ≤ i→n(i * 8) + 1, 0 < i, j + 2 ^ (i * 8 - 1) < 0, j + 2 ^ (i * 8) ≤ 0, j + 2 ^ (i * 8) < i, j + 2 ^ (i * 8) < j % 2 ^ (i * 8), 0 < j % 2 ^ (i * 8) ⊦ bits2bytes((mklist(false, i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))).rest) = fix(i→n(i) + 1, int2bytes(j % 2 ^ (i * 8))).rest, (mklist(false, i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))).rest = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 245:
⊦ i < 0 ∧ j ≠ 0 → ¬ 0 < i % j
Proof step 246:
¬(j < 0 ∧ 2 ^ (i * 8) ≠ 0), # (mklist(false, i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))).rest % 8 = 0, # int2bits(j % 2 ^ (i * 8)) ≤ i→n(i * 8) + 1, 0 < i, j + 2 ^ (i * 8 - 1) < 0, j + 2 ^ (i * 8) ≤ 0, j + 2 ^ (i * 8) < i, j + 2 ^ (i * 8) < j % 2 ^ (i * 8), 0 < j % 2 ^ (i * 8) ⊦ bits2bytes((mklist(false, i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))).rest) = fix(i→n(i) + 1, int2bytes(j % 2 ^ (i * 8))).rest, (mklist(false, i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))).rest = []

Rule argument

seq: ⊦ i < 0 ∧ j ≠ 0 → ¬ 0 < i % j subst: [j, i] → [2 ^ (i * 8), j] rotate: F spec: int-div inst: name: mod-grz-01

Additional information

Used terms: 2 ^ (i * 8), j