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 Th78:
for n being positive Nat,
    R being n-characteristic Ring holds Char R = min(CharSet R)
proof
let n be positive Nat,
    R be n-characteristic Ring;
set M = CharSet R;
A1: n = Char R by Def6;
n '*' 1.R = 0.R & n <> 0 & for m being positive Nat
   st m < n holds m '*' 1.R <> 0.R by A1,Def5;
then A2: n in M;
now let x be ExtReal;
  assume x in M;
  then consider m being positive Nat such that
  A3: x = m & m '*' 1.R = 0.R;
  thus n <= x by A3,A1,Def5;
  end;
hence thesis by A2,A1,XXREAL_2:def 7;
end;
