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Proof step 609 from proof bitsand-cast (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 610:
sgn(mklist(false, m) + false ' + true ' + bits) = false ' + true ' + bits, 2 + # bits = # bits1 ⊦ lastn(2 + # bits + m, mklist(bitsand(bits1, false ' + true ' + bits).first, m) + bitsand(bits1, false ' + true ' + bits)) = lastn(2 + # bits + m, fillsgn(2 + # bits + m, bitsand(bits2 + mklist(false, m), bits3) + bitsand(false ' + true ' + bits, bits1))), bitsand(bits1, false ' + true ' + bits) = [], bits3 + bits1 = [], bits3 = [], bits2 + mklist(false, m) = []

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m;% ⊦ (boolvar ' + bits).first ↔ boolvar;% ⊦ m ≤ m + n;% ⊦ m + n ≤ m + n0 ↔ n ≤ n0;% ⊦ boolvar ' + bits ≠ [];% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ 0 + m = m;% ⊦ n ≤ m → m + n0 - n = (m - n) + n0;% ⊦ m + n - n + n1 = m - n1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;