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Proof step 10 from proof int2bytes-rec-neg-04 (previous step)

0 < i, j0 * 2 ^ (i * 8) + 2 ^ (i * 8 - 1) < 0 ⊦ 2 ^ (i * 8) = 0, bits2bytes(int2bits(j0 * 2 ^ (i * 8))) = int2bytes(j0) + fix(i→n(i) + 1, i2b(0) ').rest

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: 0 ≤ i, j ≠ 0 ⊦ int2bits(j * 2 ^ i) = int2bits(j) + mklist(false, i→n(i)) subst: [i, j] → [i * 8, j0] rotate: F spec: int2bits inst: name: int2bits-2pot-04

Additional information

Used simplifier rules: int2bytes-byte: ~128 ≤ i, i < 128 ⊦ int2bytes((* i)) = i2b(i) ';% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i * 0 = 0;% ⊦ int2bits(0) = false ';% ⊦ i + 0 = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ ¬ 2 ^ i < 0; Used terms: i * 8, j0