let a be real number ; :: thesis: for M being non empty Reflexive symmetric bounded MetrStruct st a >= diameter ([#] M) holds
(dist_toler M,a) [*] = nabla the carrier of M
let M be non empty Reflexive symmetric bounded MetrStruct ; :: thesis: ( a >= diameter ([#] M) implies (dist_toler M,a) [*] = nabla the carrier of M )
assume A1: a >= diameter ([#] M) ; :: thesis: (dist_toler M,a) [*] = nabla the carrier of M
dist_toler M,a = (dist_toler M,a) [*] by A1, Th38;
hence (dist_toler M,a) [*] = nabla the carrier of M by A1, Th37; :: thesis: verum