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Proof step 165 from proof bitsand-cast (previous step)

¬ ( #(mklist(true, n) + bits2 + bitsand(bits, true ' + false ' + bits1)) ≤ n0 + # bits2 + # bits ∧ mklist(true, n) + bits2 + bitsand(bits, true ' + false ' + bits1) ≠ []), n0 + # bits2 + # bits = # fillsgn(n0 + # bits2 + # bits, mklist(true, n) + bits2 + bitsand(bits, true ' + false ' + bits1)), # bits = 2 + # bits1, n0 + # bits2 + # bits = # fillsgn(n0 + # bits2 + # bits, (mklist(true, n) + mklist(true, # bits2)) + true ' + false ' + bits1), sgn((mklist(true, n) + mklist(true, # bits2)) + true ' + false ' + bits1) = true ' + false ' + bits1, bits2.first, 2 + # bits1 + n < n0 + # bits ⊦ mklist(true, n0) + bits2 + bitsand(bits, true ' + false ' + bits1) = fillsgn(n0 + # bits2 + # bits, mklist(true, n) + bits2 + bitsand(bits, true ' + false ' + bits1)), bits2 = [], bits2 + bitsand(bits, true ' + false ' + bits1) = [], bits = [], bits2 + bits = [], n = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 166:
n0 + # bits2 + # bits = # fillsgn(n0 + # bits2 + # bits, mklist(true, n) + bits2 + bitsand(bits, true ' + false ' + bits1)), # bits = 2 + # bits1, n0 + # bits2 + # bits = # fillsgn(n0 + # bits2 + # bits, (mklist(true, n) + mklist(true, # bits2)) + true ' + false ' + bits1), sgn((mklist(true, n) + mklist(true, # bits2)) + true ' + false ' + bits1) = true ' + false ' + bits1, # bits < # bitsand(bits, true ' + false ' + bits1), 3 + # bits1 < # bitsand(bits, true ' + false ' + bits1), bits2.first, 2 + # bits1 + n < n0 + # bits, n0 + # bits < n + # bitsand(bits, true ' + false ' + bits1) ⊦ mklist(true, n0) + bits2 + bitsand(bits, true ' + false ' + bits1) = fillsgn(n0 + # bits2 + # bits, mklist(true, n) + bits2 + bitsand(bits, true ' + false ' + bits1)), bits2 = [], bits2 + bitsand(bits, true ' + false ' + bits1) = [], bits = [], bits2 + bits = [], n = 0

Rule argument

Additional information

Used simplifier rules: and-notempty-01: ⊦ bits ≠ [] → bitsand(bits, boolvar ' + bits0) ≠ [];% ⊦ # bits = 0 ↔ bits = [];% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ m + n < m + n0 ↔ n < n0;% ⊦ 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)% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m + n ≤ m + n0 ↔ n ≤ n0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # mklist(boolvar, n) = n;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;