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Proof step 396 from proof bitsand-cast (previous step)

#(true ' + false ' + bits) ≤ # bits1 ∧ true ' + false ' + bits ≠ [] ∧ (true ' + false ' + bits).first, sgn(mklist(true, n - 1) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits ⊦ n = 0, lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bits3 + bitsand(bits1, true ' + false ' + bits))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand((bits2 + mklist(true, n - 1)) + true ' + false ' + bits, bits3 + bits1))), bits3 = [], bits3 + bits1 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 397:
# bits1 = 2 + # bits, sgn(mklist(true, n - 1) + true ' + false ' + bits) = true ' + false ' + bits ⊦ bits3 + bits1 = [], bits3 = [], lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bits3 + bitsand(bits1, true ' + false ' + bits))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand((bits2 + mklist(true, n - 1)) + true ' + false ' + bits, bits3 + bits1))), n = 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 ≠ [];