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Proof step 152 from proof bitsand-cast (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 153:
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, fillsgn(m, bits2) + bitsand(bits, true ' + false ' + bits1)), # bits2 + # bitsand(bits, true ' + false ' + bits1) ≤ n, 2 + # bits1 + m < n, # bits2 < m, bits2.first ⊦ mklist(true, n - # bits2 + # bitsand(bits, true ' + false ' + bits1)) + bits2 + bitsand(bits, true ' + false ' + bits1) = fillsgn(n, fillsgn(m, bits2) + bitsand(bits, true ' + false ' + bits1)), bits2 + bits = [], bits = [], bits2 = [], bits2 + bitsand(bits, true ' + false ' + bits1) = []

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ∧ n = n0 → m < n0; (forward)%n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m ≤ n → (n < m ↔ false);% ⊦ # mklist(boolvar, n) = n;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits ≠ [] → ((bits + bits0).first ↔ bits.first);% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;