reserve i,s,t,m,n,k for Nat,
        c,d,e for Element of NAT,
        fn for FinSequence of NAT,
        x,y for Integer;

theorem Th6:
  for a,b be Integer,m be Nat st a*b mod m = 1 & a mod m = 1
    holds b mod m = 1
proof let a,b be Integer,m be Nat;
  assume A1:a*b mod m = 1 & a mod m = 1;
  then A2:m <> 0 by INT_1:def 10;
  then a mod m = 1 mod m by A1,PEPIN:5,INT_1:58;
  then a*b,1*b are_congruent_mod m by INT_4:11,A2,NAT_D:64;
  hence thesis by A1,NAT_D:64;
end;
