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Proof step 18 from proof ushort-band-shift (previous step)

s2i(sho) % 256 = 0, 0 ≤ (65536 + s2i(sho)) / 256, ~65536 ≤ s2i(sho), s2i(sho) < 0, ~256 < s2i(sho) ⊦ band(255, s2i(sho) / 256) = ((65536 + s2i(sho)) / 256) % 256

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
abs(i) < abs(j) ⊦ i / j = 0
Proof step 20:
abs(s2i(sho)) < abs(256), s2i(sho) % 256 = 0, 0 ≤ (65536 + s2i(sho)) / 256, ~65536 ≤ s2i(sho), s2i(sho) < 0, ~256 < s2i(sho) ⊦ band(255, 0) = ((65536 + s2i(sho)) / 256) % 256

Rule argument

seq: abs(i) < abs(j) ⊦ i / j = 0 subst: [j, i] → [256, s2i(sho)] rotate: F spec: int-div inst: name: div-zero-02

Additional information

Used simplifier rules: ⊦ i < 0 → abs(i) = ~ i;% ⊦ ~ i < j ↔ 0 < j + i;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;%i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: 256, s2i(sho)