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Proof step 98 from proof bitsand-cast (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 99:
# bits = 2 + # bits1, sgn(mklist(true, n0 - 1) + true ' + false ' + bits1) = true ' + false ' + bits1, n = # fillsgn(n, mklist(true, n0 - 1) + true ' + false ' + bits1), n0 + 1 + # bits1 < n ⊦ bits2 + bits = [], bits2 = [], lastn(n, fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1))) = lastn(n, fillsgn(n, bitsand(mklist(true, n0 - 1) + true ' + false ' + bits1, bits2 + bits))), n0 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m;% ⊦ (boolvar ' + bits).first ↔ boolvar;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits ≠ [];