reserve a,a1,a2,b,c,d for Ordinal,
  n,m,k for Nat,
  x,y,z,t,X,Y,Z for set;
reserve f,g for Function;
reserve A,B,C for array;
reserve O for connected non empty Poset;
reserve R,Q for array of O;

theorem Th49:
  [x,y] in inversions R implies [y,x] nin inversions R
  proof assume [x,y] in inversions R; then
    not y in x by Th46; then
    y nin x;
    hence [y,x] nin inversions R by Th46;
  end;
