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Proof step 46 from proof int2bytes-rec-pos-any (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 < i + 1 → i→n(i + 1) = i→n(i) + 1 subst: [i] → [i * 8] rotate: F spec: intnat inst: name: rax

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: i * 8