reserve d,i,j,k,m,n,p,q,x,k1,k2 for Nat,
  a,c,i1,i2,i3,i5 for Integer;

theorem
  c > 1 implies 1 mod c = 1
proof
  assume
A1: c > 1;
  then 1 div c = 0 by PRE_FF:4;
  then 1 mod c = 1 - 0*c by A1,INT_1:def 10;
  hence thesis;
end;
