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Proof step 57 from proof bib-pos-high (previous step)

lastn(8, int2bits(i)).first, 8 ≤ # int2bits(i), 0 < i % 256, 127 < i % 256, 127 < i, 0 < i, 0 ≤ i ⊦ i % 256 = 256 + b2i(i2b(i % 256 - 256))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 58:
~128 ≤ i, i ≤ 127 ⊦ b2i(i2b((* i))) = i
Proof step 59:
¬(~128 ≤ i % 256 - 256 ∧ i % 256 - 256 ≤ 127), lastn(8, int2bits(i)).first, 8 ≤ # int2bits(i), 0 < i % 256, 127 < i % 256, 127 < i, 0 < i, 0 ≤ i ⊦ i % 256 = 256 + b2i(i2b(i % 256 - 256))

Rule argument

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

Additional information

Used simplifier rules: ⊦ i + (j - i) = j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: i % 256 - 256