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Proof step 142 from proof bitsand-cast (previous step)

(true ' + false ' + bits1).first ∧ #(true ' + false ' + bits1) ≤ # bits ∧ true ' + false ' + bits1 ≠ [], n = # fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1)), # bits = 2 + # bits1, n = # fillsgn(n, mklist(true, m) + true ' + false ' + bits1), sgn(mklist(true, m) + true ' + false ' + bits1) = true ' + false ' + bits1, 2 + # bits1 + m < # fillsgn(m, bits2) + # bits, bits2.first, # bits2 < m, 2 + # bits1 + m < n, n < # fillsgn(m, bits2) + # bits, 3 + # bits1 + m < # fillsgn(m, bits2) + # bits ⊦ bits2 = [], bits = [], bits2 + bits = [], fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1)) = lastn(n, fillsgn(n, fillsgn(m, bits2) + bitsand(bits, true ' + false ' + bits1))), n = # fillsgn(n, fillsgn(m, bits2) + bitsand(bits, true ' + false ' + bits1))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 143:
sgn(mklist(true, m) + true ' + false ' + bits1) = true ' + false ' + bits1, n = # fillsgn(n, mklist(true, m) + true ' + false ' + bits1), # bits = 2 + # bits1, n = # fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1)), 2 + # bits1 + m < # fillsgn(m, bits2) + # bits, 2 + # bits1 + m < n, # bits2 < m, bits2.first, n < # fillsgn(m, bits2) + # bits, 3 + # bits1 + m < # fillsgn(m, bits2) + # bits ⊦ n = # fillsgn(n, fillsgn(m, bits2) + bitsand(bits, true ' + false ' + bits1)), fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1)) = lastn(n, fillsgn(n, fillsgn(m, bits2) + bitsand(bits, true ' + false ' + bits1))), bits2 + bits = [], bits = [], bits2 = []

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m;% ⊦ m +1 = m + 1;% ⊦ m < n → n ≠ 0;% ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward)% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ n < n0 ∧ n0 < n1 → n +1 < n1; (forward)% ⊦ m + n = n + m;% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ (boolvar ' + bits).first ↔ boolvar;% ⊦ boolvar ' + bits ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;