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Proof step 195 from proof bitsand-cast (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 196:
n = # fillsgn(n, mklist(false, m) + false ' + true ' + bits1), sgn(mklist(false, m) + false ' + true ' + bits1) = false ' + true ' + bits1, 2 + # bits1 = # bits, 2 + # bits1 + m < # bitsand(bits, false ' + true ' + bits1), 2 + # bits1 + m < n, n < # bitsand(bits, false ' + true ' + bits1), 3 + # bits1 + m < # bitsand(bits, false ' + true ' + bits1) ⊦ lastn(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(bits, false ' + true ' + bits1))

Rule argument

Additional information

Used simplifier rules: and-notempty-01: ⊦ bits ≠ [] → bitsand(bits, boolvar ' + bits0) ≠ [];% ⊦ m +1 = m + 1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # bits = 0 ↔ bits = [];% ⊦ 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)% ⊦ n < # bits → lastn(n, fillsgn(n, bits)) = lastn(n, bits);% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;