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Proof step 8 from proof int2bytes-rec-pos-any (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 9:
⊦ 0 < j ∧ 0 < i → ¬ i→n(i) + 1 < # int2bits(j % 2 ^ i)
Proof step 10:
0 < j ∧ 0 < i * 8 → ¬ i→n(i * 8) + 1 < # int2bits(j % 2 ^ (i * 8)), 2 ^ (i * 8) ≤ j, 0 < i ⊦ bits2bytes(int2bits(j / 2 ^ (i * 8)) + fillsgn(i→n(i * 8) + 1, int2bits(j % 2 ^ (i * 8))).rest) = int2bytes(j / 2 ^ (i * 8)) + fix(i→n(i) + 1, int2bytes(j % 2 ^ (i * 8))).rest, # fillsgn(i→n(i * 8 + 1), int2bits(j % 2 ^ (i * 8))).rest % 8 = 0 ∧ fillsgn(i→n(i * 8 + 1), int2bits(j % 2 ^ (i * 8))).rest ≠ []

Rule argument

seq: ⊦ 0 < j ∧ 0 < i → ¬ i→n(i) + 1 < # int2bits(j % 2 ^ i) subst: [j, i] → [j, i * 8] rotate: F spec: int2bits inst: name: int2bits-len-mod2pot

Additional information

Used terms: j, i * 8