let V be RealLinearSpace; :: thesis: for w, y being VECTOR of V
for a, b, c, d being Element of (DTrSpace (V,w,y)) st a,b // c,d holds
( c,d // a,b & b,a // d,c )
let w, y be VECTOR of V; :: thesis: for a, b, c, d being Element of (DTrSpace (V,w,y)) st a,b // c,d holds
( c,d // a,b & b,a // d,c )
let a, b, c, d be Element of (DTrSpace (V,w,y)); :: thesis: ( a,b // c,d implies ( c,d // a,b & b,a // d,c ) )
reconsider u = a, v = b, u1 = c, v1 = d as VECTOR of V ;
assume a,b // c,d ; :: thesis: ( c,d // a,b & b,a // d,c )
then u,v,u1,v1 are_DTr_wrt w,y by Th44;
then ( v,u,v1,u1 are_DTr_wrt w,y & u1,v1,u,v are_DTr_wrt w,y ) by Th21, Th22;
hence ( c,d // a,b & b,a // d,c ) by Th44; :: thesis: verum