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Proof step 375 from proof bitsand-cast (previous step)

n ≠ 0, sgn((mklist(boolvar, n -1) + boolvar ') + boolvar0 ' + bits) = boolvar ' + boolvar0 ' + bits ⊦ lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(boolvar ' + boolvar0 ' + bits, bits0))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(bits2 + (mklist(boolvar, n -1) + boolvar ') + boolvar0 ' + bits, bits0))), n = 0, boolvar ↔ boolvar0, bits0 = [], ¬ false ∈ mklist(boolvar, n -1) + boolvar ' ∧ boolvar0 ∧ ¬ false ∈ bits, ¬ true ∈ mklist(boolvar, n -1) + boolvar ' ∧ ¬ boolvar0 ∧ ¬ true ∈ bits

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ bits = bits0 + boolvar ' + bits1 → boolvar ∈ bits;% ⊦ bits = bits0 + boolvar ' + bits1 → boolvar ∈ bits; (forward)% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)% ⊦ ¬ true ∈ mklist(false, n);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ ¬ false ∈ mklist(true, n);% ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ n -1 = n - 1;