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Proof step 236 from proof bitsand-cast (previous step)

¬ true ∈ mklist(false, m) ∧ # bits2 < # mklist(false, m) ∧ ¬ bits2.first ∧ mklist(false, m) ≠ [] ∧ bits2 ≠ [], n0 + # bits = # fillsgn(n0 + # bits, mklist(false, # bits2) + bitsand(bits, false ' + true ' + bits1)), n0 + # bits = # fillsgn(n0 + # bits, mklist(false, m) + false ' + true ' + bits1), sgn(mklist(false, m) + false ' + true ' + bits1) = false ' + true ' + bits1, 2 + # bits1 = # bits, # bits2 < m, 2 + # bits1 + m < n0 + # bits ⊦ mklist(false, n0) + bitsand(bits, false ' + true ' + bits1) = fillsgn(n0 + # bits, mklist(false, # bits2) + bitsand(bits, false ' + true ' + bits1)), bits2 + bits = [], bits2 = [], bits = [], bits2.first

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 237:
2 + # bits1 = # bits, n0 + # bits = # fillsgn(n0 + # bits, mklist(false, m) + false ' + true ' + bits1), n0 + # bits = # fillsgn(n0 + # bits, mklist(false, # bits2) + bitsand(bits, false ' + true ' + bits1)), 2 + # bits1 + m < n0 + # bits, # bits2 < m ⊦ bits2 = [], bits = [], bits2 + bits = [], mklist(false, n0) + bitsand(bits, false ' + true ' + bits1) = fillsgn(n0 + # bits, mklist(false, # bits2) + bitsand(bits, false ' + true ' + bits1)), bits2.first

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ ¬ true ∈ mklist(false, n);% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ # mklist(boolvar, n) = n;% ⊦ m < n → n ≠ 0;% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ sgn(false ' + true ' + bits) = false ' + true ' + bits;% ⊦ ¬ true ∈ bits → sgn(bits + false ' + bits0) = sgn(false ' + bits0);