reserve I for set,
  x,x1,x2,y,z for set,
  A for non empty set;
reserve C,D for Category;
reserve a,b,c,d for Object of C;
reserve f,g,h,i,j,k,p1,p2,q1,q2,i1,i2,j1,j2 for Morphism of C;
reserve f for Morphism of a,b,
        g for Morphism of b,a;
reserve g for Morphism of b,c;
reserve f,g for Morphism of C;

theorem Th62:
  for F being Injections_family of c,I st x in I holds cod(F/.x) = c
proof
  let F be Injections_family of c,I such that
A1: x in I;
  (cods F)/.x = (I --> c)/.x by Def16;
  hence cod(F/.x) = (I --> c)/.x by A1,Def2
    .= c by A1,Th2;
end;
