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Proof step 17 from proof bitsand-cast (previous step)

false ∈ bits, n = # fillsgn(n, bits), true ∈ bits, # bits < n, false ∈ bits → bits = mklist(boolvar, n0) + boolvar0 ' + bits1 ∧ sgn(mklist(boolvar, n0) + boolvar0 ' + bits1) = boolvar ' + boolvar0 ' + bits1 ∧ ¬(boolvar ↔ boolvar0) ∧ n0 ≠ 0 ⊦ lastn(n, fillsgn(n, bitsand(sgn(bits), bits0))) = lastn(n, fillsgn(n, bitsand(bits, bits0))), bits = [], bits0 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
n = # fillsgn(n, mklist(boolvar, n0) + boolvar0 ' + bits1), sgn(mklist(boolvar, n0) + boolvar0 ' + bits1) = boolvar ' + boolvar0 ' + bits1, n0 + 1 + # bits1 < n ⊦ lastn(n, fillsgn(n, bitsand(boolvar ' + boolvar0 ' + bits1, bits0))) = lastn(n, fillsgn(n, bitsand(mklist(boolvar, n0) + boolvar0 ' + bits1, bits0))), bits0 = [], n0 = 0, boolvar ↔ boolvar0, ¬ false ∈ mklist(boolvar, n0) ∧ boolvar0 ∧ ¬ false ∈ bits1, ¬ true ∈ mklist(boolvar, n0) ∧ ¬ boolvar0 ∧ ¬ true ∈ bits1

Rule argument

Additional information

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