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Proof step 23 from proof band-011x-neg (previous step)

bitsand(false ' + mklist(true, i→n(i)), false ' + bits0) = false ' + bits, sgn(bitsinvert(uint2bits(~ j)) +1) = false ' + bits0, false ∈ bitsinvert(uint2bits(~ j)) +1, j < i, 0 ≤ i, j < 0 ⊦ (j + 1) % 2 ^ i + 2 ^ i = 1 + bits2uint(bits), bitsinvert(uint2bits(~ j)) +1 = []

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 < j → sgn(bitsinvert(uint2bits(j)) +1) ≠ false + bits subst: [j, bits] → [~ j, bits0] rotate: F spec: int2bits inst: name: sgn-first

Additional information

Used simplifier rules: ⊦ 0 < ~ i ↔ i < 0;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ boolvar + bits = boolvar ' + bits; Used terms: ~ j, bits0