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Proof step 372 from proof bitsand-cast (previous step)

false ∈ bits1, true ∈ bits1, false ∈ bits1 → bits1 = mklist(boolvar, n) + boolvar0 ' + bits ∧ sgn(mklist(boolvar, n) + boolvar0 ' + bits) = boolvar ' + boolvar0 ' + bits ∧ ¬(boolvar ↔ boolvar0) ∧ n ≠ 0 ⊦ bits2 + bits1 = [], bits0 = [], lastn(# bits1, fillsgn(# bits1, bitsand(sgn(bits1), bits0))) = lastn(# bits1, fillsgn(# bits1, bitsand(bits2 + bits1, bits0)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 373:
sgn(mklist(boolvar, n) + boolvar0 ' + bits) = boolvar ' + boolvar0 ' + bits ⊦ lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(boolvar ' + boolvar0 ' + bits, bits0))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(bits2 + mklist(boolvar, n) + boolvar0 ' + bits, bits0))), n = 0, boolvar ↔ boolvar0, bits0 = [], ¬ false ∈ mklist(boolvar, n) ∧ boolvar0 ∧ ¬ false ∈ bits, ¬ true ∈ mklist(boolvar, n) ∧ ¬ boolvar0 ∧ ¬ true ∈ bits

Rule argument

Additional information

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