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Proof step 17 from proof band-011x-is-unsigned (previous step)

i→n(i) < # int2bits(j), 0 ≤ i, 0 < i, j < 0, 0 ≤ j + 2 ^ (i - 1), 0 ≤ 2 ^ i + j ⊦ fillsgn(i→n(i), int2bits(j)) = [], j + 2 ^ i = bits2int(fillsgn(i→n(i), int2bits(j))) + 2 ^ n→i(# fillsgn(i→n(i), int2bits(j)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ i < ~1 → (m < # int2bits(i) ↔ ¬ 0 ≤ i + 2 ^ (n→i(m) - 1))
Proof step 19:
¬ j < ~1, i→n(i) < # int2bits(j), 0 ≤ i, 0 < i, j < 0, 0 ≤ j + 2 ^ (i - 1), 0 ≤ 2 ^ i + j ⊦ fillsgn(i→n(i), int2bits(j)) = [], j + 2 ^ i = bits2int(fillsgn(i→n(i), int2bits(j))) + 2 ^ n→i(# fillsgn(i→n(i), int2bits(j)))

Rule argument

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

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ 0 < i → n→i(i→n(i)) = i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: j, i→n(i)