reserve p,p1,p2,p3,q,q1,q2 for Point of TOP-REAL 2,
  i for Nat,
  lambda for Real;

theorem
  for a,b,c,d being Real st a<=b & c <=d
  holds SW-corner rectangle(a,b,c,d) = |[a,c]|
proof
  let a,b,c,d be Real;
  set K=rectangle(a,b,c,d);
  assume that
A1: a<=b and
A2: c <=d;
A3: SW-corner K= |[W-bound K, S-bound K]| by PSCOMP_1:def 11;
  W-bound K=a by A1,A2,Th36;
  hence thesis by A1,A2,A3,Th39;
end;
