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;
