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Proof step 171 from proof bitsand-cast (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 172:
sgn((mklist(true, n) + mklist(true, # bits2)) + true ' + false ' + bits1) = true ' + false ' + bits1, n0 + # bits2 + # bits = # fillsgn(n0 + # bits2 + # bits, (mklist(true, n) + mklist(true, # bits2)) + true ' + false ' + bits1), # bits = 2 + # bits1, n ≤ n0, 2 + # bits1 + n < n0 + # bits, bits2.first ⊦ mklist(true, n0) = mklist(true, n0 - n) + mklist(true, n), mklist(true, n) + bits2 + bitsand(bits, true ' + false ' + bits1) = [], n = 0, bits2 + bits = [], bits = [], bits2 + bitsand(bits, true ' + false ' + bits1) = [], bits2 = []

Rule argument

Additional information

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