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Proof step 239 from proof bitsand-cast (previous step)

¬ ( #(mklist(false, # bits2) + bitsand(bits, false ' + true ' + bits1)) ≤ n0 + # bits ∧ mklist(false, # bits2) + bitsand(bits, false ' + true ' + bits1) ≠ []), 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 240:
n0 + # bits = # fillsgn(n0 + # bits, mklist(false, # bits2) + bitsand(bits, false ' + true ' + bits1)), n0 + # bits = # fillsgn(n0 + # bits, mklist(false, m) + false ' + true ' + bits1), 2 + # bits1 = # bits, 2 + # bits1 + m < # bits2 + # bitsand(bits, false ' + true ' + bits1), # bits2 < m, 2 + # bits1 + m < n0 + # bits, n0 + # bits < # bits2 + # bitsand(bits, false ' + true ' + bits1), 3 + # bits1 + m < # bits2 + # bitsand(bits, false ' + true ' + bits1) ⊦ mklist(false, n0) + bitsand(bits, false ' + true ' + bits1) = fillsgn(n0 + # bits, mklist(false, # bits2) + bitsand(bits, false ' + true ' + bits1)), bits2 + bits = [], bits = [], bits2 = [], bits2.first

Rule argument

Additional information

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