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Proof step 23 from proof bitsinvert-size (previous step)

bitsinvert(bits0) = (¬ boolvar)' + bits, # sgn(bitsinvert(bits0)) = # sgn(bits0), boolvar ∈ bits0 ⊦ bits0 = [], # sgn(bits0) = # sgn(boolvar ' + bits0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
bits ≠ [], bits.first ↔ boolvar ⊦ sgn(boolvar ' + bits) = sgn(bits)
Proof step 25:
¬(bits0 ≠ [] ∧ (bits0.first ↔ boolvar)), bitsinvert(bits0) = (¬ boolvar)' + bits, # sgn(bitsinvert(bits0)) = # sgn(bits0), boolvar ∈ bits0 ⊦ bits0 = [], # sgn(bits0) = # sgn(boolvar ' + bits0)

Rule argument

name: sgn-rec-01 rotate: F subst: [bits, boolvar] → [bits0, boolvar]

Additional information

Used terms: bits0, boolvar