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Proof step 10 from proof bib-on-bits (previous step)

8 < # int2bits(i), ~128 ≤ i, i ≤ 0 ⊦ i = bits2int(lastn(8, int2bits(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) - 1))
Proof step 12:
¬ i < ~1, 8 < # int2bits(i), ~128 ≤ i, i ≤ 0 ⊦ i = bits2int(lastn(8, int2bits(i)))

Rule argument

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

Additional information

Used simplifier rules: ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: i, 8