reserve a,b,c,d,m,x,n,j,k,l for Nat,
  t,u,v,z for Integer,
  f,F for FinSequence of NAT;
reserve p,q,r,s for real number;
reserve a,b,c,d,m,x,n,k,l for Nat,
  t,z for Integer,
  f,F,G for FinSequence of REAL;
reserve q,r,s for real number;
reserve D for set;

theorem Th45:
  a<>0 implies ((a,b) In_Power m).1 <> 0
  proof
    assume
    A1: a<>0;
    ((a,b) In_Power m).1 = a |^m by NEWTON:28;
    hence thesis by A1;
  end;
