reserve S for non empty satisfying_CongruenceIdentity
              satisfying_SegmentConstruction
              satisfying_BetweennessIdentity
              satisfying_Pasch
              TarskiGeometryStruct;
reserve a,b for POINT of S;
reserve A for Subset of S;
reserve S for non empty satisfying_Tarski-model
              TarskiGeometryStruct;
reserve a,b,c,m,r,s for POINT of S;
reserve A for Subset of S;
reserve S         for non empty satisfying_Lower_Dimension_Axiom
                                satisfying_Tarski-model
                                TarskiGeometryStruct,
        a,b,c,d,m,p,q,r,s,x for POINT of S,
        A,A9,E              for Subset of S;

theorem Th62:
  a,a,a,b are_coplanar
  proof
    per cases;
    suppose a = b;
      hence thesis by Th61;
    end;
    suppose a <> b;
      then consider a9 be POINT of S such that
A1:   not Collinear a,b,a9 by GTARSKI3:92;
      ex E be Subset of S st Plane(a,b,a9) = E & E is_plane & a in E &
        b in E & a9 in E by A1,Th49;
      hence thesis;
    end;
  end;
