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Proof step 10 from proof sgn-zeros (previous step)

bits0 + false ' = boolvar + bits2 ∧ bits0 + false ' ≠ [], ∀ bits. sgn(bits0 + false ' + bits) = sgn(false ' + bits) ⊦ sgn(bits0 + false ' + bits1) = sgn(false ' + bits1), true ∈ bits0, boolvar

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

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