reserve p,q for Rational;
reserve g,m,m1,m2,n,n1,n2 for Nat;
reserve i,i1,i2,j,j1,j2 for Integer;
reserve R for Ring, F for Field;

theorem Th79:
for R being Ring holds Char R = min*(CharSet R)
proof
let R be Ring;
set n = Char R;
per cases;
suppose A1: Char R = 0;
  then CharSet R = {} by Th77;
  hence thesis by A1,NAT_1:def 1;
  end;
suppose Char R > 0;
  then reconsider n1 = n as positive Nat;
  reconsider R1 = R as n1-characteristic Ring by Def6;
  A2: Char R = Char R1 = min(CharSet R1) by Th78;
  then A3: n in CharSet R by XXREAL_2:def 7;
  for k being Nat st k in CharSet R holds n <= k by A2,XXREAL_2:def 7;
  hence thesis by A3,NAT_1:def 1;
  end;
end;
