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Proof step 40 from proof bib-neg-low (previous step)

9 < # int2bits(j), i0 < 0, 256 * i0 + j < 0, j < 0, ~256 < j, 256 * i0 + j < ~128, j < ~128 ⊦ int2bits(j).rest = [], 8 = # fillsgn(8, int2bits(j).rest), b2i(i2b(bits2int(lastn(8, int2bits(i0 - 1) + fillsgn(8, int2bits(j).rest))))) = 256 + j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 41:
⊦ i < ~1 → (m < # int2bits(i) ↔ ¬ 0 ≤ i + 2 ^ (n→i(m) - 1))

Rule argument

seq: ⊦ i < ~1 → (m < # int2bits(i) ↔ ¬ 0 ≤ i + 2 ^ (n→i(m) - 1)) subst: [i, m] → [j, 9] rotate: F spec: int2bits inst: name: int2bits-lslen-05

Additional information

Used simplifier rules: j0 ≠ 0, j < j0 ⊦ i < (* j) → i < (* j0);% ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i; Used terms: j, 9