let p1, p2 be Point of (TOP-REAL 2); :: thesis: for a, b, c, d being real number st a < b & c < d & p1 `1 = b & p2 `2 = c & c <= p1 `2 & p1 `2 <= d & a < p2 `1 & p2 `1 <= b holds
LE p1,p2, rectangle a,b,c,d
let a, b, c, d be real number ; :: thesis: ( a < b & c < d & p1 `1 = b & p2 `2 = c & c <= p1 `2 & p1 `2 <= d & a < p2 `1 & p2 `1 <= b implies LE p1,p2, rectangle a,b,c,d )
set K = rectangle a,b,c,d;
assume A1: ( a < b & c < d & p1 `1 = b & p2 `2 = c & c <= p1 `2 & p1 `2 <= d & a < p2 `1 & p2 `1 <= b ) ; :: thesis: LE p1,p2, rectangle a,b,c,d
then A2: ( p1 in LSeg |[b,d]|,|[b,c]| & p2 in LSeg |[b,c]|,|[a,c]| ) by Th1, JGRAPH_6:10;
W-min (rectangle a,b,c,d) = |[a,c]| by A1, JGRAPH_6:56;
then (W-min (rectangle a,b,c,d)) `1 = a by EUCLID:56;
hence LE p1,p2, rectangle a,b,c,d by A1, A2, JGRAPH_6:71; :: thesis: verum