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Proof step 431 from proof bitsand-cast (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 432:
sgn((mklist(true, n) + mklist(true, # bits3)) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits, # bits1 ≤ 2 + # bits + n, bits3.first ⊦ lastn(2 + # bits + n + # bits3, mklist(true, 2 + # bits + n - # bits1) + bits3 + bitsand(bits1, true ' + false ' + bits)) = lastn(2 + # bits + n + # bits3, fillsgn(2 + # bits + n + # bits3, bits2 + mklist(true, n) + bits3 + bitsand(bits1, true ' + false ' + bits))), bits3 + bitsand(bits1, true ' + false ' + bits) = [], bits2 + mklist(true, n) + mklist(true, # bits3) = [], bits3 = [], bits3 + bits1 = [], bits1 = []

Rule argument

Additional information

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