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Proof step 16 from proof sgn-last-diff (previous step)

⊦ sgn((¬ boolvar)' + boolvar ') = sgn((¬ boolvar)' + bits0) + boolvar ', boolvar ∈ bits0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ bits ≠ [] ∧ (bits.first ↔ ¬ boolvar) → sgn(boolvar ' + bits) = boolvar ' + bits
Proof step 18:
boolvar ' ≠ [] ∧ (boolvar '.first ↔ ¬ ¬ boolvar) ⊦ (¬ boolvar)' + boolvar ' = sgn((¬ boolvar)' + bits0) + boolvar ', boolvar ∈ bits0

Rule argument

name: sgn-base-03 rotate: F subst: [bits, boolvar] → [boolvar ', ¬ boolvar]

Additional information

Used simplifier rules: ⊦ boolvar ' ≠ [];% ⊦ boolvar '.first ↔ boolvar; Used terms: boolvar ', ¬ boolvar