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Proof step 10 from proof bib-neg-high (previous step)

i ≤ ~256, ~128 ≤ i % 256, i < 0 ⊦ b2i(i2b(bits2int(lastn(8, int2bits(i))))) = i % 256, lastn(8, int2bits(i)).first ∧ 8 ≤ # int2bits(i) ∧ ~256 ≠ i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ i < ~1 → (m ≤ # int2bits(i) ↔ ¬ 0 ≤ i + 2 ^ (n→i(m) - 2))
Proof step 12:
i < ~1, i ≤ ~256, ~128 ≤ i % 256, i < 0 ⊦ b2i(i2b(bits2int(lastn(8, int2bits(i))))) = i % 256, lastn(8, int2bits(i)).first ∧ ¬ 0 ≤ i + 2 ^ (n→i(8) - 2) ∧ ~256 ≠ i

Rule argument

spec: int2bits inst: name: int2bits-lelen-05 seq: ⊦ i < ~1 → (m ≤ # int2bits(i) ↔ ¬ 0 ≤ i + 2 ^ (n→i(m) - 2)) subst: [i, m] → [i, 8] flags: rewrite

Additional information

Used simplifier rules: numlsledel: j0 ≠ 0, j < j0 ⊦ i ≤ (* j) → i < (* j0); from specification int-abs Used terms: i, 8