
theorem Th2:
  proj(1,1) qua Function" is Function of REAL,REAL 1 &
  proj(1,1) qua Function" is one-to-one &
  dom(proj(1,1) qua Function") = REAL &
  rng(proj(1,1) qua Function") = REAL 1 &
  ex g be Function of REAL,REAL 1 st g is bijective
  & proj(1,1) qua Function" = g
proof
A1: REAL 1 = rng(W) by Lm1,FUNCT_1:33;
  REAL = dom(W) by Lm1,FUNCT_1:33;
  then reconsider g=W as Function of REAL,REAL 1 by A1,FUNCT_2:1;
  g is onto by A1,FUNCT_2:def 3;
  hence thesis by Lm1,FUNCT_1:33;
end;
