let p, q be Point of (TOP-REAL 2); :: thesis: ( p `1 <= q `1 implies W-bound (LSeg (p,q)) = p `1 )
assume A1: p `1 <= q `1 ; :: thesis: W-bound (LSeg (p,q)) = p `1
then A2: proj1 .: (LSeg (p,q)) = [.(p `1),(q `1).] by Th52;
thus W-bound (LSeg (p,q)) = lower_bound (proj1 .: (LSeg (p,q))) by Th43
.= p `1 by A1, A2, JORDAN5A:19 ; :: thesis: verum