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Proof step 17 from proof sgn-append-03 (previous step)

bits0 + bits1 = boolvar1 + bits, bits0 = [] ∨ (∀ bits1, boolvar. sgn(bits0 + bits1) = sgn((¬ boolvar)' + bits1) ∨ boolvar ∈ bits0) ⊦ sgn(bits0 + bits1) = sgn((¬ boolvar0)' + bits1), boolvar0 ↔ boolvar1, bits0 + bits1 = [], boolvar0 ∈ bits0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
bits0 + bits1 = boolvar1 ' + bits, bits0 = [] ∨ (∀ bits1, boolvar. sgn(bits0 + bits1) = sgn((¬ boolvar)' + bits1) ∨ boolvar ∈ bits0) ⊦ bits0 + bits1 = [], boolvar0 ↔ boolvar1, sgn(bits0 + bits1) = sgn((¬ boolvar0)' + bits1), boolvar0 ∈ bits0, ¬ boolvar1 ∈ bits0 ∧ ¬ boolvar1 ∈ bits1

Rule argument

Additional information

Used simplifier rules: ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)% ⊦ boolvar + bits = boolvar ' + bits;