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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
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)

Rule argument

Additional information

Used simplifier rules: ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ boolvar ' + bits ≠ [];% ⊦ bits2uint(false ' + bits) = bits2uint(bits);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)% ⊦ boolvar + bits = boolvar ' + bits;