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Proof step 407 from proof bitsand-cast (previous step)

n = m + 1, sgn(mklist(true, m) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits ⊦ lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bits3 + bitsand(bits1, true ' + false ' + bits))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(bits3, bits2 + mklist(true, m)) + bitsand(bits1, true ' + false ' + bits))), n = 0, bits3 + bits1 = [], bits1 = [], bits2 + mklist(true, m) = [], bits3 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 408:
sgn(mklist(true, m) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits ⊦ bits3 + bits1 = [], bits1 = [], bits2 + mklist(true, m) = [], bits3 = [], lastn(2 + # bits + m, fillsgn(2 + # bits + m, bits3 + bitsand(bits1, true ' + false ' + bits))) = lastn(2 + # bits + m, fillsgn(2 + # bits + m, bitsand(bits3, bits2 + mklist(true, m)) + bitsand(bits1, true ' + false ' + bits)))

Rule argument

Additional information

Used simplifier rules: ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ bits = bits0 + boolvar ' + bits1 → boolvar ∈ bits;% ⊦ bits = bits0 + boolvar ' + bits1 → boolvar ∈ bits; (forward)% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + 1 ≠ 0;