theorem
  proj2. |[r,s]| = s & proj1. |[r,s]| = r
proof
  thus proj2. |[r,s]| = |[r,s]|`2 by Def6
    .= s by EUCLID:52;
  thus proj1. |[r,s]| = |[r,s]|`1 by Def5
    .= r by EUCLID:52;
end;
