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Proof step 3 from proof int2bytes-rec-pos-any (previous step)

2 ^ (i * 8) ≤ j, 0 < i ⊦ bits2bytes(int2bits(j)) = 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 4:
⊦ 2 ^ i ≤ j ∧ 0 < i → int2bits(j) = int2bits(j / 2 ^ i) + fillsgn(i→n(i + 1), int2bits(j % 2 ^ i)).rest
Proof step 5:
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

Rule argument

seq: ⊦ 2 ^ i ≤ j ∧ 0 < i → int2bits(j) = int2bits(j / 2 ^ i) + fillsgn(i→n(i + 1), int2bits(j % 2 ^ i)).rest subst: [i, j] → [i * 8, j] rotate: F spec: int2bits inst: name: int2bits-rec-2pot-pos

Additional information

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