reserve a,b,c for set;
reserve r for Real,
  X for set,
  n for Element of NAT;

theorem
  weight Sorgenfrey-line = continuum
proof
  thus weight Sorgenfrey-line c= continuum by Lm5,Lm6,Th20,WAYBEL23:73;
  consider B being Basis of Sorgenfrey-line such that
A1: weight Sorgenfrey-line = card B by WAYBEL23:74;
  assume not continuum c= weight Sorgenfrey-line;
  then
A2: weight Sorgenfrey-line in continuum by CARD_1:4;
  the carrier of Sorgenfrey-line = REAL by Def2;
  then consider x being Real, q being Rational such that
  x < q and
A3: not [.x,q.[ in UniCl B by A2,A1,Th32;
  [.x,q.[ is open Subset of Sorgenfrey-line by Th11;
  then [.x,q.[ in the topology of Sorgenfrey-line by PRE_TOPC:def 2;
  hence thesis by A3,YELLOW_9:22;
end;
