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Proof step 11 from proof shiftright-neg-mone (previous step)

i→n(j) < # int2bits(i), i < 0, 0 ≤ 2 ^ (abs(j) - 1) + i ⊦ bits2int(firstn(# int2bits(i), mklist(true, i→n(j)) + int2bits(i))) = ~1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ i < ~1 → (m < # int2bits(i) ↔ ¬ 0 ≤ i + 2 ^ (n→i(m) - 1))
Proof step 13:
¬ i < ~1, i→n(j) < # int2bits(i), i < 0, 0 ≤ 2 ^ (abs(j) - 1) + i ⊦ bits2int(firstn(# int2bits(i), mklist(true, i→n(j)) + int2bits(i))) = ~1

Rule argument

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

Additional information

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