reserve p, q for Point of TOP-REAL 2,
  r for Real,
  h for non constant standard special_circular_sequence,
  g for FinSequence of TOP-REAL 2,
  f for non empty FinSequence of TOP-REAL 2,
  I, i1, i, j, k for Nat;

theorem Th12:
  1 <= i & i <= len h implies W-bound L~h <= (h/.i)`1 & (h/.i)`1 <= E-bound L~h
proof
A1: len h > 4 by GOBOARD7:34;
  assume that
A2: 1<=i and
A3: i<=len h;
  i in dom h by A2,A3,FINSEQ_3:25;
  then h/.i in L~h by A1,GOBOARD1:1,XXREAL_0:2;
  hence thesis by PSCOMP_1:24;
end;
