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Proof step 5 from proof int2bytes-rec-pos-any (previous step)

2 ^ (i * 8) ≤ j ∧ 0 < 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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ # bits0 % 8 = 0 ∧ bits ≠ [] ∧ bits0 ≠ [] → bits2bytes(bits + bits0) = bits2bytes(bits) + bits2bytes(bits0)
Proof step 7:
¬ ( # fillsgn(i→n(i * 8 + 1), int2bits(j % 2 ^ (i * 8))).rest % 8 = 0 ∧ int2bits(j / 2 ^ (i * 8)) ≠ [] ∧ fillsgn(i→n(i * 8 + 1), int2bits(j % 2 ^ (i * 8))).rest ≠ []), 2 ^ (i * 8) ≤ j ∧ 0 < 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
Proof step 51:
# fillsgn(i→n(i * 8 + 1), int2bits(j % 2 ^ (i * 8))).rest % 8 = 0 ∧ int2bits(j / 2 ^ (i * 8)) ≠ [] ∧ fillsgn(i→n(i * 8 + 1), int2bits(j % 2 ^ (i * 8))).rest ≠ [], 2 ^ (i * 8) ≤ j ∧ 0 < i * 8, 2 ^ (i * 8) ≤ j, 0 < i ⊦ bits2bytes(int2bits(j / 2 ^ (i * 8))) + bits2bytes(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

Rule argument

name: bits2bytes-app rotate: F subst: [bits0, bits] → [fillsgn(i→n(i * 8 + 1), int2bits(j % 2 ^ (i * 8))).rest, int2bits(j / 2 ^ (i * 8))]

Additional information

Used terms: fillsgn(i→n(i * 8 + 1), int2bits(j % 2 ^ (i * 8))).rest, int2bits(j / 2 ^ (i * 8))