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Proof step 176 from proof bitsand-cast (previous step)

¬(#(false ' + true ' + bits1) = # bits ∧ mklist(false, n0 - 1) ≠ [] ∧ bits2 ≠ [] ∧ false ' + true ' + bits1 ≠ []), 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 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 177:
n = # fillsgn(n, false ' + true ' + bits1), # bits = 2 + # bits1, n0 - 1 = 0, n0 + 1 + # bits1 < n ⊦ lastn(n, fillsgn(n, bitsand(bits, false ' + true ' + bits1))) = lastn(n, fillsgn(n, bitsand(false ' + true ' + bits1, bits2 + bits))), bits2 = [], bits2 + bits = [], n0 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1;% ⊦ sgn(false ' + true ' + bits) = false ' + true ' + bits;% ⊦ [] + bits = bits;% ⊦ mklist(boolvar, 0) = [];% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ bits = bits0 + boolvar ' + bits1 → boolvar ∈ bits; (forward)% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)% ⊦ boolvar ' ≠ [];% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;