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Proof step 211 from proof bitsand-cast (previous step)

mklist(false, m) ≠ [] ∧ bits2 ≠ [], 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, 2 + # bits1 + m < n, n < (2 + # bits1) + # bitsand(bits2, mklist(false, m)), m + 1 < # bitsand(bits2, mklist(false, m)), m < # bitsand(bits2, mklist(false, m)) ⊦ bitsand(bits2, mklist(false, m)) = [], fillsgn(n, bitsand(bits, false ' + true ' + bits1)) = lastn(n, fillsgn(n, bitsand(bits2, mklist(false, m)) + bitsand(bits, false ' + true ' + bits1))), bits2 + bits = [], bits2 = [], m = 0, bits = [], n = # fillsgn(n, bitsand(bits2, mklist(false, m)) + bitsand(bits, false ' + true ' + bits1))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: and-notempty: ⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) ≠ [];%n0 < n ⊦ m + (* n) < m0 + (* n0) ↔ m + (n - n0) < m0;% ⊦ m + n < m + n0 ↔ n < n0;% ⊦ m +1 = m + 1;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;%n < n0 ⊦ (* n) ≠ m0 + (* n0);% ⊦ # bits = 0 ↔ bits = [];% ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward)% ⊦ n < n0 ∧ n0 < n1 → n +1 < n1; (forward)% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ mklist(boolvar, m) = [] ↔ m = 0;