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Proof step 155 from proof bitsand-cast (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 156:
n = # fillsgn(n, fillsgn(m, bits2) + bitsand(bits, true ' + false ' + bits1)), # bits = 2 + # bits1, n = # fillsgn(n, mklist(true, m) + true ' + false ' + bits1), sgn(mklist(true, m) + true ' + false ' + bits1) = true ' + false ' + bits1, bits2.first, # bits2 < m, 2 + # bits1 + m < n, # bits2 + # bits ≤ n ⊦ bits2 + bitsand(bits, true ' + false ' + bits1) = [], bits2 = [], bits = [], bits2 + bits = [], mklist(true, n - # bits2 + # bits) + bits2 + bitsand(bits, true ' + false ' + bits1) = fillsgn(n, fillsgn(m, bits2) + bitsand(bits, true ' + false ' + bits1))

Rule argument

Additional information

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