X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground_2%2Frelocation%2Frtmap_pushs.ma;h=dd88b8c35e5351708d52bf31afbd50bdef1d93e3;hb=2976c347e18717e691825ebdf73a5ce941c57d1b;hp=f64590e7ad3a4fad5c1c8fd1b51d4b29a843ab59;hpb=199ba569adf94f9948053352c2c0a1c6deb62bc5;p=helm.git

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 f64590e7a..dd88b8c35 100644
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_pushs.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_pushs.ma
@@ -12,30 +12,48 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground_2/notation/functions/liftstar_2.ma".
+include "ground_2/notation/functions/upspoonstar_2.ma".
 include "ground_2/relocation/rtmap_eq.ma".
 
 (* RELOCATION MAP ***********************************************************)
 
 rec definition pushs (f:rtmap) (n:nat) on n: rtmap ≝ match n with
-[ O ⇒ f | S m ⇒ ↑(pushs f m) ].
+[ O ⇒ f | S m ⇒ ⫯(pushs f m) ].
 
-interpretation "pushs (rtmap)" 'LiftStar n f = (pushs f n).
+interpretation "pushs (rtmap)" 'UpSpoonStar 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.
+lemma pushs_O: ∀f. f = ⫯*[0] f.
 // qed.
 
-lemma pushs_S: ∀f,n. ↑↑*[n] f = ↑*[⫯n] f.
+lemma pushs_S: ∀f,n. ⫯⫯*[n] f = ⫯*[↑n] f.
 // qed.
 
-lemma pushs_eq_repl: ∀n. eq_repl (λf1,f2. ↑*[n] f1 ≗ ↑*[n] f2).
+lemma pushs_eq_repl: ∀n. eq_repl (λf1,f2. ⫯*[n] f1 ≡ ⫯*[n] f2).
 #n elim n -n /3 width=5 by eq_push/
 qed.
 
-(* Advancedd properties *****************************************************)
+(* Advanced properties ******************************************************)
 
-lemma pushs_xn: ∀n,f. ↑*[n] ↑f = ↑*[⫯n] f.
+lemma pushs_xn: ∀n,f. ⫯*[n] ⫯f = ⫯*[↑n] f.
 #n elim n -n //
 qed.