End REC_INC_ALT.
Section REC_INC_RELAT.
(* sur la relation parent *)
Variable c0 : Config.
Variable s1 s2 : Site.
Remark rinc_trans_parent :
forall s3 s4 : Site,
parent (rec_inc_trans c0 s1 s2) s4 s3 -> parent c0 s4 s3.

Lemma rinc_trans_parent_cr :
forall s3 s4 : Site,
(parent c0 s3 s4 -> dt c0 s3 < dt c0 s4) ->
parent (rec_inc_trans c0 s1 s2) s3 s4 ->
dt (rec_inc_trans c0 s1 s2) s3 < dt (rec_inc_trans c0 s1 s2) s4.