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;
reserve A for array, B for permutation of A;

theorem Th86:
  for A being 0-based finite non empty array of O
  ex B being permutation of A st B is ascending
  proof
    let A be 0-based finite non empty array of O;
    consider C being 0-based arr_computation of A such that
A1: C is complete by Th85;
    C is finite by Th76; then
    reconsider B = last C as permutation of A by Th78;
    take B;
    thus B is ascending by A1;
  end;
