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;
reserve T for non empty array of O;
reserve p,q,r,s for Element of dom T;

theorem
  for R being finite array of O st [x,y] in inversions R
  holds card inversions Swap(R,x,y) < card inversions R
proof let R being finite array of O such that
A1: [x,y] in inversions R;
  card inversions Swap(R,x,y) in Segm card inversions R  by A1,Th73;
 hence card inversions Swap(R,x,y) < card inversions R  by NAT_1:44;
end;
