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Proof step 689 from proof bitsand-cast (previous step)

¬ ( #(mklist(false, # bits3) + bitsand(bits1, false ' + true ' + bits)) ≤ 2 + # bits + m ∧ mklist(false, # bits3) + bitsand(bits1, false ' + true ' + bits) ≠ []), 2 + # bits + m = # fillsgn(2 + # bits + m, mklist(false, # bits3) + bitsand(bits1, false ' + true ' + bits)), # bits1 = 2 + # bits, # bits3 < m ⊦ bits1 = [], bits3 = [], bits3 + bits1 = [], bits2 + mklist(false, m) = [], mklist(false, m) + bitsand(bits1, false ' + true ' + bits) = fillsgn(2 + # bits + m, mklist(false, # bits3) + bitsand(bits1, false ' + true ' + bits)), # bits3 = m, bits3.first

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 690:
# bits1 = 2 + # bits, 2 + # bits + m = # fillsgn(2 + # bits + m, mklist(false, # bits3) + bitsand(bits1, false ' + true ' + bits)), 2 + # bits + m < # bits3 + # bitsand(bits1, false ' + true ' + bits), # bits3 < m ⊦ # bits3 = m, mklist(false, m) + bitsand(bits1, false ' + true ' + bits) = fillsgn(2 + # bits + m, mklist(false, # bits3) + bitsand(bits1, false ' + true ' + bits)), bits2 + mklist(false, m) = [], bits3 + bits1 = [], bits3 = [], bits1 = [], bits3.first

Rule argument

Additional information

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