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Proof step 3 from proof byte-unsigned (previous step)

0 ≤ i, 0 < i, i < 256, 128 ≤ i ⊦ b2i(i2b(i)) = b2i(i2b(i - 256)), i2b(i) = i2b(i - 256)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
~128 ≤ i, i ≤ 127 ⊦ b2i(i2b((* i))) = i
Proof step 5:
~128 ≤ i - 256 ∧ i - 256 ≤ 127, 0 ≤ i, 0 < i, i < 256, 128 ≤ i ⊦ b2i(i2b(i)) = i - 256, i2b(i) = i2b(i - 256)

Rule argument

name: num-ibbi rotate: F subst: [i] → [i - 256]

Additional information

Used simplifier rules: byte-equal: ⊦ b2i(byi) = b2i(byj) ↔ byi = byj;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ i - j ≤ i0 ↔ i ≤ j + i0;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j ∧ ¬ i0 < j → ¬ i0 < i; Used terms: i - 256