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Proof step 422 from proof bitsand-cast (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 423:
# bits1 = 2 + # bits, sgn((mklist(true, n) + mklist(true, # bits3)) + true ' + false ' + bits) = true ' + false ' + bits, bits3.first ⊦ lastn(2 + # bits + n + # bits3, fillsgn(2 + # bits + n + # bits3, bits3 + bitsand(bits1, true ' + false ' + bits))) = lastn(2 + # bits + n + # bits3, fillsgn(2 + # bits + n + # bits3, bits2 + mklist(true, n) + bits3 + bitsand(bits1, true ' + false ' + bits))), bits1 = [], bits3 + bits1 = [], bits3 = [], bits2 + mklist(true, n) + mklist(true, # bits3) = []

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 ≤ m + n;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ mklist(boolvar, m + n) = mklist(boolvar, m) + mklist(boolvar, n);