reserve a,b,i,j,k,l,m,n for Nat;

theorem PRA:
  for n be Nat, a be Real holds Product((a,a)Subnomial n) = a|^(n*(n+1))
  proof
    let n be Nat, a be Real;
    set f = (n+1) |-> (a|^n),h = the_value_of f,i = len f;
    Product((a,a)Subnomial n) = Product f by CONST1
    .= h|^ i by RVSUM_3:8
    .= a|^(n*(n+1)) by NEWTON:9;
    hence thesis;
  end;
