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Proof step 189 from proof bitsand-cast (previous step)

n0 = m + 1, n = # fillsgn(n, mklist(false, m) + false ' + true ' + bits1), sgn(mklist(false, m) + false ' + true ' + bits1) = false ' + true ' + bits1, 2 + # bits1 = # bits, n0 + 1 + # bits1 < n ⊦ n0 = 0, lastn(n, fillsgn(n, bitsand(bits, false ' + true ' + bits1))) = lastn(n, fillsgn(n, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1))), bits2 + bits = [], bits2 = [], m = 0, bits = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 190:
n = # fillsgn(n, mklist(false, m) + false ' + true ' + bits1), sgn(mklist(false, m) + false ' + true ' + bits1) = false ' + true ' + bits1, 2 + # bits1 = # bits, 2 + # bits1 + m < n ⊦ lastn(n, fillsgn(n, bitsand(bits, false ' + true ' + bits1))) = lastn(n, fillsgn(n, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1))), bits2 + bits = [], bits2 = [], m = 0, 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)% ⊦ (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;