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Proof step 22 from proof band-011x-neg (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
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 = []

Rule argument

Additional information

Used simplifier rules: ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ bits ≠ [] → (boolvar ∈ sgn(bits) ↔ boolvar ∈ bits);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)% ⊦ sgn(bits) = [] ↔ bits = [];% ⊦ boolvar + bits = boolvar ' + bits;