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 Th60:
  for n be prime Nat holds n divides a+b iff n divides a|^n + b|^n
  proof
    let n be prime Nat;
    n divides a|^n - a & n divides b|^n - b by Th58; then
    A1: n divides (a|^n - a) + (b|^n - b) by WSIERP_1:4;
    A2: a|^n + b|^n = (a+b) + ((a|^n + b|^n) - (a + b));
    hence n divides a+b implies n divides a|^n + b|^n by A1,WSIERP_1:4;
    assume n divides a|^n + b|^n;
    hence thesis by A1,A2,INT_2:1;
  end;
