let a be Real; :: thesis: for M being non empty Reflexive symmetric bounded MetrStruct st a >= diameter ([#] M) holds
dist_toler (M,a) = (dist_toler (M,a)) [*]
let M be non empty Reflexive symmetric bounded MetrStruct ; :: thesis: ( a >= diameter ([#] M) implies dist_toler (M,a) = (dist_toler (M,a)) [*] )
assume A1: a >= diameter ([#] M) ; :: thesis: dist_toler (M,a) = (dist_toler (M,a)) [*]
(dist_toler (M,a)) [*] c= nabla the carrier of M ;
then ( dist_toler (M,a) c= (dist_toler (M,a)) [*] & (dist_toler (M,a)) [*] c= dist_toler (M,a) ) by A1, Th37, LANG1:18;
hence dist_toler (M,a) = (dist_toler (M,a)) [*] by XBOOLE_0:def 10; :: thesis: verum