reserve i,j,k,n for Nat,
  X,Y,a,b,c,x for set,
  r,s for Real;
reserve f,g for FinSequence of TOP-REAL 2;
reserve f for non constant standard special_circular_sequence,
  p,p1,p2,q for Point of TOP-REAL 2;
reserve G for Go-board;

theorem Th19:
  j <= width G implies h_strip(G,j) is convex
proof
  assume
A1: j<= width G;
  set P = h_strip(G,j);
  let w1,w2 be Point of TOP-REAL 2 such that
A2: w1 in P & w2 in P;
  w1`2 <= w2`2 or w2`2 <= w1`2;
  hence thesis by A1,A2,Lm4;
end;
