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 Th75:
  {[a,R]} is arr_computation of R
  proof
    reconsider C = {[a,R]} as a-based non empty array;
    C is arr_computation of R
    proof
A1:   dom C = {a} & a in {a} by FUNCT_5:12,TARSKI:def 1; then
      base-C = a by Def4;
      hence C.(base-C) = R by GRFUNC_1:6;
      hereby let b; assume
        b in dom C; then
        a = b by A1,TARSKI:def 1;
        hence C.b is array of O by GRFUNC_1:6;
      end;
      let b; assume
      b in dom C & succ b in dom C; then
      a = b & a = succ b by A1,TARSKI:def 1; then
      a in a by ORDINAL1:6;
      hence thesis;
    end;
    hence thesis;
  end;
