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 Th97:
for F being Field holds canHom_Int F = (canHom_Rat F) | INT
proof
 let F be Field;
 set f = canHom_Int F;
 set g = canHom_Rat F;
 dom g = RAT by FUNCT_2:def 1;
 then
A1: dom(g|INT) = INT by RELAT_1:62,NUMBERS:14;
 now
  let x be object;
  assume
A2: x in dom f;
  then reconsider y = x as Element of INT.Ring;
  reconsider r = y as Element of F_Rat by NUMBERS:14;
A3: f.1_I = 1_F by GROUP_1:def 13;
  thus f.x = (f.numerator r) / 1_F by RAT_1:17
  .= (f.numerator r) / (f.denominator r) by A3,RAT_1:17
  .= g.x by Def11
  .= (g|INT).x by A2,FUNCT_1:49;
 end;
 hence thesis by FUNCT_2:def 1,A1;
end;
