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Proof step 39 from proof int2bytes-rec-pos-any (previous step)

i→n(i * 8 + 1) = # int2bits(j % 2 ^ (i * 8)), int2bits(j % 2 ^ (i * 8)).rest = [], 0 < j, 2 ^ (i * 8) ≤ j, 0 < i, 0 ≤ i, 0 ≤ j, i→n(i * 8 + 1) ≤ 1 + 8 * i→n(i) ⊦ bits2bytes(int2bits(j / 2 ^ (i * 8)) + (mklist(¬ 0 ≤ j % 2 ^ (i * 8), 1 + 8 * i→n(i) - 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 40:
⊦ int2bits(j).rest = [] ↔ j = 0 ∨ j = ~1
Proof step 41:
i→n(i * 8 + 1) = # int2bits(j % 2 ^ (i * 8)), j % 2 ^ (i * 8) = 0 ∨ j % 2 ^ (i * 8) = ~1, 0 < j, 2 ^ (i * 8) ≤ j, 0 < i, 0 ≤ i, 0 ≤ j, i→n(i * 8 + 1) ≤ 1 + 8 * i→n(i) ⊦ bits2bytes(int2bits(j / 2 ^ (i * 8)) + (mklist(¬ 0 ≤ j % 2 ^ (i * 8), 1 + 8 * i→n(i) - 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

seq: ⊦ int2bits(j).rest = [] ↔ j = 0 ∨ j = ~1 subst: [j] → [j % 2 ^ (i * 8)] rotate: F spec: int2bits inst: name: int2bits-rest

Additional information

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