let n be non zero Nat; RLSStruct(# the carrier of (TOP-REAL n), the ZeroF of (TOP-REAL n), the addF of (TOP-REAL n), the Mult of (TOP-REAL n) #) = RLSStruct(# the carrier of (TOP-REAL-INFTY n), the ZeroF of (TOP-REAL-INFTY n), the addF of (TOP-REAL-INFTY n), the Mult of (TOP-REAL-INFTY n) #)
RLSStruct(# the carrier of (TOP-REAL n), the ZeroF of (TOP-REAL n), the addF of (TOP-REAL n), the Mult of (TOP-REAL n) #) = RealVectSpace (Seg n)
by EUCLID:def 8;
hence
RLSStruct(# the carrier of (TOP-REAL n), the ZeroF of (TOP-REAL n), the addF of (TOP-REAL n), the Mult of (TOP-REAL n) #) = RLSStruct(# the carrier of (TOP-REAL-INFTY n), the ZeroF of (TOP-REAL-INFTY n), the addF of (TOP-REAL-INFTY n), the Mult of (TOP-REAL-INFTY n) #)
by Def8; verum