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Proof step 9 from proof bitsinvert-size (previous step)

bitsinvert(bits0) = boolvar0 ' + bits, # sgn(bitsinvert(bits0)) = # sgn(bits0), (¬ boolvar0) ∈ bits0 ⊦ boolvar0 ↔ ¬ boolvar, bits0 = [], # sgn((¬ boolvar)' + bitsinvert(bits0)) = # sgn(boolvar ' + bits0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ bits ≠ [] ∧ (bits.first ↔ ¬ boolvar) → sgn(boolvar ' + bits) = boolvar ' + bits
Proof step 11:
¬(bitsinvert(bits0) ≠ [] ∧ (bitsinvert(bits0).first ↔ ¬ ¬ boolvar)), bitsinvert(bits0) = boolvar0 ' + bits, # sgn(bitsinvert(bits0)) = # sgn(bits0), (¬ boolvar0) ∈ bits0 ⊦ boolvar0 ↔ ¬ boolvar, bits0 = [], # sgn((¬ boolvar)' + bitsinvert(bits0)) = # sgn(boolvar ' + bits0)
Proof step 13:
bitsinvert(bits0) ≠ [] ∧ (bitsinvert(bits0).first ↔ ¬ ¬ boolvar), bitsinvert(bits0) = boolvar0 ' + bits, # sgn(bitsinvert(bits0)) = # sgn(bits0), (¬ boolvar0) ∈ bits0 ⊦ boolvar0 ↔ ¬ boolvar, bits0 = [], #((¬ boolvar)' + bitsinvert(bits0)) = # sgn(boolvar ' + bits0)

Rule argument

name: sgn-base-03 rotate: F subst: [bits, boolvar] → [bitsinvert(bits0), ¬ boolvar]

Additional information

Used terms: bitsinvert(bits0), ¬ boolvar