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diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_isuni.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_isuni.ma
index efde1a120..38443bf59 100644
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_isuni.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_isuni.ma
@@ -13,13 +13,13 @@
 (**************************************************************************)
 
 include "ground_2/notation/relations/isuniform_1.ma".
-include "ground_2/relocation/rtmap_isid.ma".
+include "ground_2/relocation/rtmap_isfin.ma".
 
 (* RELOCATION MAP ***********************************************************)
 
 inductive isuni: predicate rtmap ≝
 | isuni_isid: ∀f. 𝐈⦃f⦄ → isuni f
-| isuni_next: ∀f. isuni f → ∀g. ⫯f = g → isuni g
+| isuni_next: ∀f. isuni f → ∀g. ↑f = g → isuni g
 .
 
 interpretation "test for uniformity (rtmap)"
@@ -27,19 +27,30 @@ interpretation "test for uniformity (rtmap)"
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma isuni_inv_push: ∀g. 𝐔⦃g⦄ → ∀f. ↑f = g → 𝐈⦃f⦄.
+lemma isuni_inv_push: ∀g. 𝐔⦃g⦄ → ∀f. ⫯f = g → 𝐈⦃f⦄.
 #g * -g /2 width=3 by isid_inv_push/
 #f #_ #g #H #x #Hx destruct elim (discr_push_next … Hx)
 qed-.
 
-lemma isuni_inv_next: ∀g. 𝐔⦃g⦄ → ∀f. ⫯f = g → 𝐔⦃f⦄.
+lemma isuni_inv_next: ∀g. 𝐔⦃g⦄ → ∀f. ↑f = g → 𝐔⦃f⦄.
 #g * -g #f #Hf
 [ #x #Hx elim (isid_inv_next … Hf … Hx)
 | #g #H #x #Hx destruct /2 width=1 by injective_push/
 ]
 qed-.
 
+lemma isuni_split: ∀g. 𝐔⦃g⦄ → (∃∃f. 𝐈⦃f⦄ & ⫯f = g) ∨ (∃∃f.𝐔⦃f⦄ & ↑f = g).
+#g #H elim (pn_split g) * #f #Hf
+/4 width=3 by isuni_inv_next, isuni_inv_push, or_introl, or_intror, ex2_intro/
+qed-.
+
 (* basic forward lemmas *****************************************************)
 
-lemma isuni_fwd_push: ∀g. 𝐔⦃g⦄ → ∀f. ↑f = g → 𝐔⦃f⦄.
+lemma isuni_fwd_push: ∀g. 𝐔⦃g⦄ → ∀f. ⫯f = g → 𝐔⦃f⦄.
 /3 width=3 by isuni_inv_push, isuni_isid/ qed-.
+
+(* Forward lemmas with test for finite colength *****************************)
+
+lemma isuni_fwd_isfin: ∀f. 𝐔⦃f⦄ → 𝐅⦃f⦄.
+#f #H elim H -f /3 width=1 by isfin_next, isfin_isid/
+qed-.