- more results on relocation

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / relocation / rtmap_pushs.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_pushs.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_pushs.ma
index 9772f34bdff0119077f6fee6625c7643f732131d..a1e7ab669ee0ab7583d81fc2954f76d405eacfef 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_pushs.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_pushs.ma
@@ -22,6 +22,24 @@ rec definition pushs (f:rtmap) (n:nat) on n: rtmap ≝ match n with
 
 interpretation "pushs (rtmap)" 'LiftStar n f = (pushs f n).
 
+(* Basic_inversion lemmas *****************************************************)
+
+lemma eq_inv_pushs_sn: ∀n,f1,g2. ↑*[n] f1 ≗ g2 →
+                       ∃∃f2. f1 ≗ f2 & ↑*[n] f2 = g2.
+#n elim n -n /2 width=3 by ex2_intro/
+#n #IH #f1 #g2 #H elim (eq_inv_px … H) -H [|*: // ]
+#f0 #Hf10 #H1 elim (IH … Hf10) -IH -Hf10 #f2 #Hf12 #H2 destruct
+/2 width=3 by ex2_intro/
+qed-.
+
+lemma eq_inv_pushs_dx: ∀n,f2,g1. g1 ≗ ↑*[n] f2 →
+                       ∃∃f1. f1 ≗ f2 & ↑*[n] f1 = g1.
+#n elim n -n /2 width=3 by ex2_intro/
+#n #IH #f2 #g1 #H elim (eq_inv_xp … H) -H [|*: // ]
+#f0 #Hf02 #H1 elim (IH … Hf02) -IH -Hf02 #f1 #Hf12 #H2 destruct
+/2 width=3 by ex2_intro/
+qed-.
+
 (* Basic properties *********************************************************)
 
 lemma pushs_O: ∀f. f = ↑*[0] f.