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Proof step 35 from proof bib-pos-high (previous step)

# int2bits(j) < 9, 0 < i0, 0 < i0 * 256 + j, 0 ≤ j, 0 < j, j < 256, 64 ≤ i0 * 256 + j, 127 < i0 * 256 + j, 127 < j, 0 ≤ i0 ⊦ 0 = i0 * 256 + j, j = b2i(i2b(bits2int(lastn(8, int2bits(i0) + fillsgn(9, int2bits(j)).rest)))) + 256, lastn(8, int2bits(i0) + fillsgn(9, int2bits(j)).rest).first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 36:
⊦ 0 < i → (# int2bits(i) < m ↔ i < 2 ^ (n→i(m) - 2))

Rule argument

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

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;%j0 ≠ 0, j < j0 ⊦ i < (* j) → i < (* j0);% ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) Used terms: 9, j