let n be Nat; :: thesis: the carrier of (n -VectSp_over F_Real) = the carrier of (TOP-REAL n)
thus the carrier of (n -VectSp_over F_Real) = n -tuples_on the carrier of F_Real by MATRIX13:102
.= REAL n by EUCLID:def 1, VECTSP_1:def 15
.= the carrier of (TOP-REAL n) by EUCLID:25 ; :: thesis: verum