let p, q be Point of (TOP-REAL 2); :: thesis: ( p `1 <= q `1 implies E-bound (LSeg p,q) = q `1 )
assume A1: p `1 <= q `1 ; :: thesis: E-bound (LSeg p,q) = q `1
then A2: proj1 .: (LSeg p,q) = [.(p `1 ),(q `1 ).] by Th60;
thus E-bound (LSeg p,q) = upper_bound (proj1 .: (LSeg p,q)) by Th51
.= q `1 by A1, A2, JORDAN5A:20 ; :: thesis: verum