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Proof step 3 from proof inv-sgn (previous step)

bitsinvert(sgn(bits0)) = sgn(bitsinvert(bits0)) ⊦ bitsinvert(sgn(boolvar ' + bits0)) = sgn((¬ boolvar)' + bitsinvert(bits0))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
bits ≠ [], bits.first ↔ boolvar ⊦ sgn(boolvar ' + bits) = sgn(bits)
Proof step 5:
¬(bits0 ≠ [] ∧ (bits0.first ↔ boolvar)), bitsinvert(sgn(bits0)) = sgn(bitsinvert(bits0)) ⊦ bitsinvert(sgn(boolvar ' + bits0)) = sgn((¬ boolvar)' + bitsinvert(bits0))
Proof step 9:
bits0 ≠ [] ∧ (bits0.first ↔ boolvar), bitsinvert(sgn(bits0)) = sgn(bitsinvert(bits0)) ⊦ bitsinvert(sgn(bits0)) = sgn((¬ boolvar)' + bitsinvert(bits0))

Rule argument

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

Additional information

Used terms: bits0, boolvar