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Proof step 8 from proof shiftright-byte-8-neg-01 (previous step)

0 ≤ j, 0 < j, b2i(by) < 0, 8 ≤ j ⊦ (b2i(by) / 256 - 1) >> (j - 8) = ~1, b2i(by) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
abs(i) < abs(j) ⊦ i / j = 0
Proof step 10:
abs(b2i(by)) < abs(256), 0 ≤ j, 0 < j, b2i(by) < 0, 8 ≤ j ⊦ (0 - 1) >> (j - 8) = ~1, b2i(by) = 0

Rule argument

seq: abs(i) < abs(j) ⊦ i / j = 0 subst: [j, i] → [256, b2i(by)] rotate: F spec: int-div inst: name: div-zero-02

Additional information

Used simplifier rules: byte-nle-02: i < ~128 ⊦ ¬ b2i(by) ≤ (* i);% ⊦ i < 0 → abs(i) = ~ i;% ⊦ ~ i < j ↔ 0 < j + i;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: 256, b2i(by)