let g be non constant standard clockwise_oriented special_circular_sequence; :: thesis: E-bound (L~ g) = E-bound (RightComp g)
set A = (Cl (RightComp g)) \ (RightComp g);
A1: L~ g = (Cl (RightComp g)) \ (RightComp g) by Th29;
then reconsider A = (Cl (RightComp g)) \ (RightComp g) as non empty Subset of (TOP-REAL 2) ;
A2: proj1 .: (Cl (RightComp g)) = proj1 .: (L~ g) by Th39;
Cl (RightComp g) is compact by Th42;
then ( RightComp g c= Cl (RightComp g) & Cl (RightComp g) is Bounded ) by PRE_TOPC:48;
then A3: RightComp g is Bounded by JORDAN2C:16;
( E-bound A = sup (proj1 .: A) & E-bound (Cl (RightComp g)) = sup (proj1 .: (Cl (RightComp g))) ) by SPRECT_1:51;
hence E-bound (L~ g) = E-bound (RightComp g) by A1, A2, A3, TOPREAL6:95; :: thesis: verum