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Proof step 173 from proof bitsand-cast (previous step)

#(boolvar ' + boolvar0 ' + bits1) ≤ # bits ∧ boolvar ' + boolvar0 ' + bits1 ≠ [] ∧ ¬ (boolvar ' + boolvar0 ' + bits1).first, # bits = 2 + # bits1, sgn(mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1) = boolvar ' + boolvar0 ' + bits1, n = # fillsgn(n, mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1), n0 + 1 + # bits1 < n ⊦ bits2 = [], lastn(n, fillsgn(n, bitsand(bits, boolvar ' + boolvar0 ' + bits1))) = lastn(n, fillsgn(n, bitsand(mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1, bits2 + bits))), n0 = 0, boolvar ↔ boolvar0, bits2 + bits = [], boolvar ∧ boolvar0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 174:
n = # fillsgn(n, mklist(false, n0 - 1) + false ' + true ' + bits1), sgn(mklist(false, n0 - 1) + false ' + true ' + bits1) = false ' + true ' + bits1, # bits = 2 + # bits1, n0 + 1 + # bits1 < n ⊦ n0 = 0, lastn(n, fillsgn(n, bitsand(bits, false ' + true ' + bits1))) = lastn(n, fillsgn(n, bitsand(mklist(false, n0 - 1) + false ' + true ' + bits1, bits2 + bits))), bits2 = [], bits2 + 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;% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ bits = bits0 + boolvar ' + bits1 → boolvar ∈ bits; (forward)% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)% ⊦ m ≤ m;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ (boolvar ' + bits).first ↔ boolvar;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits ≠ [];