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Proof step 217 from proof bitsand-cast (previous step)

bits2 ≠ [] ∧ mklist(false, m) ≠ [], n = # fillsgn(n, bitsand(bits, false ' + true ' + bits1)), n = # fillsgn(n, mklist(false, m) + false ' + true ' + bits1), sgn(mklist(false, m) + false ' + true ' + bits1) = false ' + true ' + bits1, # bits2 < # bitsand(mklist(false, m), bits2), # bits2 < m, m < # bitsand(mklist(false, m), bits2), m + 1 < # bitsand(mklist(false, m), bits2), n < (2 + # bits1) + # bitsand(mklist(false, m), bits2), 2 + # bits1 + m < n, # bits2 + 1 < # bitsand(mklist(false, m), bits2) ⊦ bitsand(mklist(false, m), bits2) = [], fillsgn(n, bitsand(bits, false ' + true ' + bits1)) = lastn(n, fillsgn(n, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1))), bits2 + bits = [], bits = [], n = # fillsgn(n, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1)), bits2 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 218:
sgn(mklist(false, m) + false ' + true ' + bits1) = false ' + true ' + bits1, n = # fillsgn(n, mklist(false, m) + false ' + true ' + bits1), n = # fillsgn(n, bitsand(bits, false ' + true ' + bits1)), # bits2 < # bitsand(mklist(false, m), bits2), 2 + # bits1 + m < n, n < (2 + # bits1) + # bitsand(mklist(false, m), bits2), m + 1 < # bitsand(mklist(false, m), bits2), m < # bitsand(mklist(false, m), bits2), # bits2 < m, # bits2 + 1 < # bitsand(mklist(false, m), bits2) ⊦ bits2 = [], n = # fillsgn(n, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1)), bits = [], bits2 + bits = [], fillsgn(n, bitsand(bits, false ' + true ' + bits1)) = lastn(n, fillsgn(n, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1)))

Rule argument

Additional information

Used simplifier rules: and-notempty: ⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) ≠ [];% ⊦ m +1 = m + 1;% ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward)% ⊦ n < n0 ∧ n0 < n1 → n +1 < n1; (forward)% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m < n → n ≠ 0;% ⊦ mklist(boolvar, m) = [] ↔ m = 0;