reserve m,n,i,i2,j for Nat,
  r,r1,r2,s,t for Real,
  x,y,z for object;
reserve p,p1,p2,p3,q,q1,q2,q3,q4 for Point of TOP-REAL n;
reserve u for Point of Euclid n;
reserve R for Subset of TOP-REAL n;
reserve P,Q for Subset of TOP-REAL n;
reserve D for non vertical non horizontal non empty compact Subset of TOP-REAL
  2;

theorem Th75:
  LeftComp SpStSeq D c= UBD (L~SpStSeq D)
proof
  set f=SpStSeq D;
  set A=L~SpStSeq D;
  LeftComp f is_a_component_of A` & not LeftComp f is bounded by Th74,
GOBOARD9:def 1;
  then
A1: LeftComp f is_outside_component_of A;
  LeftComp f c= union{B where B is Subset of TOP-REAL 2: B
  is_outside_component_of A}
  proof
    let x be object;
    assume
A2: x in LeftComp f;
    LeftComp f in {B where B is Subset of TOP-REAL 2: B
    is_outside_component_of A} by A1;
    hence thesis by A2,TARSKI:def 4;
  end;
  hence thesis;
end;
