theorem :: AOFA_L00:151

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 x, y being Element of 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 s being SortSymbol of S1 st L is subst-correct & L is subst-eq-correct & L is subst-correct3 & L is vf-eq-correct & x in X . s & y in X . s & x <> y holds
\for (x,(\ex (y,(x '=' (y,L))))) in G1