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Proof step 187 from proof bitsand-cast (previous step)

false ' + true ' + bits1 ≠ [] ∧ bits ≠ [], n = # fillsgn(n, mklist(false, n0 - 1) + false ' + true ' + bits1), sgn(mklist(false, n0 - 1) + 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, n0 - 1), bits2) + bitsand(bits, false ' + true ' + bits1))), bits2 + bits = [], bits2 = [], n0 - 1 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 188:
n = # fillsgn(n, mklist(false, n0 - 1) + false ' + true ' + bits1), sgn(mklist(false, n0 - 1) + 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, n0 - 1), bits2) + bitsand(bits, false ' + true ' + bits1))), bits2 + bits = [], bits2 = [], n0 - 1 = 0, bits = []

Rule argument

Additional information

Used simplifier rules: ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits ≠ [];