theorem ThOne: :: AOFA_L00:147

for n being non empty Nat
for J being non empty non void Signature
for T being non-empty MSAlgebra over J
for X being empty-yielding GeneratorSet of T
for S1 being non empty non void b₂ -extension b₁ PC-correct QC-correct QCLangSignature over Union X
for L being non-empty Language of X extended_by ({}, the carrier of S1),S1
for G1 being QC-theory_with_equality of L
for s1 being SortSymbol of S1
for t1, t2 being Element of L,s1 st L is subst-eq-correct & L is vf-finite & L is subst-correct2 & L is subst-correct3 & s1 in the carrier of J & X . s1 is infinite holds
(t1 '=' (t2,L)) \imp (t2 '=' (t1,L)) in G1