Section Case2_.
Hypothesis Even_u : even u.
Remark Alt_v : alt b v.
End Case2_.
(* We recall from the prelude the definition of the conditional : Definition IF := [P,Q,R:Prop](P /\ Q) \/ ((~P) /\ R) Syntax IF "IF _ then _ else _" *)

Lemma Main : IF opposite u v then paired w else paired (rotate w).