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Proof step 55 from proof int2bytes-rec-neg-06 (previous step)

j0 < 0, 0 < 2 ^ (i * 8) + j0, 0 < i, j0 < ~1, 2 ^ (i * 8 - 1) + j0 < 0 ⊦ j0 = 0, 2 ^ (i * 8) = 0, j0 = ~1, i2b(~1) ' = int2bytes((1 + j0) / 2 ^ (i * 8) - 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: abs(i) < abs(j) ⊦ i / j = 0 subst: [j, i] → [2 ^ (i * 8), 1 + j0] rotate: F spec: int-div inst: name: div-zero-02

Additional information

Used simplifier rules: int2bytes-byte: ~128 ≤ i, i < 128 ⊦ int2bytes((* i)) = i2b(i) ';% ⊦ by ' = by0 ' ↔ by = by0;% ⊦ i < 0 → abs(i + 1) = abs(i) - 1;% ⊦ i < 0 → abs(i) = ~ i;% ⊦ ~ i - j = ~(i + j);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ abs(2 ^ i) = 2 ^ i;% ⊦ ~ i < j ↔ 0 < j + i;% ⊦ 0 < i ∧ 0 < j → 0 < i + j; Used terms: 2 ^ (i * 8), 1 + j0