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Proof step 53 from proof rightshift-8-02 (previous step)

int2bytes(i) = by ', i % 256 = 0, i < 0, i < ~128, ~256 ≤ i ⊦ i / 256 = ~1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 54:
abs(i) < abs(j) ⊦ i / j = 0
Proof step 55:
abs(i) < abs(256), int2bytes(i) = by ', i % 256 = 0, i < 0, i < ~128, ~256 ≤ i ⊦ 0 = ~1

Rule argument

seq: abs(i) < abs(j) ⊦ i / j = 0 subst: [j, i] → [256, i] rotate: F spec: int-div inst: name: div-zero-02

Additional information

Used simplifier rules: int2bytes-minus-256: ⊦ int2bytes(~256) = i2b(~1) ' + i2b(0) ';% ⊦ i < 0 → abs(i) = ~ i;% ⊦ ~ i < j ↔ 0 < j + i;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ by ' = by0 ' + bytes ↔ by = by0 ∧ bytes = [];% ⊦ by ' ≠ [];% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1; Used terms: 256, i