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Proof step 104 from proof bitsand-cast (previous step)

¬(# bits = #(true ' + false ' + bits1) ∧ bits2 ≠ [] ∧ mklist(true, n0 - 1) ≠ [] ∧ bits ≠ []), # bits = 2 + # bits1, sgn(mklist(true, n0 - 1) + true ' + false ' + bits1) = true ' + false ' + bits1, n = # fillsgn(n, mklist(true, n0 - 1) + true ' + false ' + bits1), n0 + 1 + # bits1 < n ⊦ bits2 = [], lastn(n, fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1))) = lastn(n, fillsgn(n, bitsand(bits2 + bits, mklist(true, n0 - 1) + true ' + false ' + bits1))), n0 = 0, bits2 + bits = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 105:
n = # fillsgn(n, true ' + false ' + bits1), n0 - 1 = 0, # bits = 2 + # bits1, n0 + 1 + # bits1 < n ⊦ lastn(n, fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1))) = lastn(n, fillsgn(n, bitsand(bits2 + bits, true ' + false ' + bits1))), n0 = 0, bits2 + bits = [], bits = [], bits2 = []

Rule argument

Additional information

Used simplifier rules: ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1;% ⊦ sgn(true ' + false ' + bits) = true ' + false ' + bits;% ⊦ [] + bits = bits;% ⊦ mklist(boolvar, 0) = [];% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ bits = bits0 + boolvar ' + bits1 → boolvar ∈ bits; (forward)% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0;% ⊦ # [] = 0;% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ m + n = n + m;