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Proof step 208 from proof bitsand-cast (previous step)

sgn(mklist(false, m) + false ' + true ' + bits1) = false ' + true ' + bits1, n = # fillsgn(n, mklist(false, m) + false ' + true ' + bits1), n = # fillsgn(n, bitsand(bits, false ' + true ' + bits1)), 2 + # bits1 + m < (2 + # bits1) + # bitsand(mklist(false, m), bits2), m + 1 < # bitsand(mklist(false, m), bits2), 2 + # bits1 + m < n, m < # bitsand(mklist(false, m), bits2), n < (2 + # bits1) + # bitsand(mklist(false, m), bits2), 3 + # bits1 + m < (2 + # bits1) + # bitsand(mklist(false, m), bits2) ⊦ n = # fillsgn(n, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1)), bits = [], m = 0, bits2 = [], bits2 + bits = [], fillsgn(n, bitsand(bits, false ' + true ' + bits1)) = lastn(n, fillsgn(n, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1))), bitsand(mklist(false, m), bits2) = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 209:
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(mklist(false, m), bits2), m + 1 < # bitsand(mklist(false, m), bits2), m < # bitsand(mklist(false, m), bits2) ⊦ bitsand(mklist(false, m), bits2) = [], fillsgn(n, bitsand(bits, false ' + true ' + bits1)) = lastn(n, fillsgn(n, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1))), bits2 + bits = [], bits2 = [], m = 0, bits = [], n = # fillsgn(n, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1))

Rule argument

Additional information

Used simplifier rules: ⊦ m +1 = m + 1;%n < n0 ⊦ (* n) ≠ m0 + (* n0);% ⊦ 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)%n0 < n ⊦ m + (* n) < m0 + (* n0) ↔ m + (n - n0) < m0;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n < m + n0 ↔ n < n0;