milestone update in ground_2 and basic_2A

[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..dd88b8c35e5351708d52bf31afbd50bdef1d93e3 100644 (file)
--- 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 â\87\92 f | S m â\87\92 â\86\91(pushs f m) ].
+[ O â\87\92 f | S m â\87\92 ⫯(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: â\88\80f. f = â\86\91*[0] f.
+lemma pushs_O: â\88\80f. f = ⫯*[0] f.
 // qed.
 
-lemma pushs_S: â\88\80f,n. â\86\91â\86\91*[n] f = â\86\91*[⫯n] f.
+lemma pushs_S: â\88\80f,n. ⫯⫯*[n] f = ⫯*[â\86\91n] f.
 // qed.
 
-lemma pushs_eq_repl: â\88\80n. eq_repl (λf1,f2. â\86\91*[n] f1 â\89\97 â\86\91*[n] f2).
+lemma pushs_eq_repl: â\88\80n. eq_repl (λf1,f2. ⫯*[n] f1 â\89¡ ⫯*[n] f2).
 #n elim n -n /3 width=5 by eq_push/
 qed.
 
 (* Advanced properties ******************************************************)
 
-lemma pushs_xn: â\88\80n,f. â\86\91*[n] â\86\91f = â\86\91*[⫯n] f.
+lemma pushs_xn: â\88\80n,f. ⫯*[n] ⫯f = ⫯*[â\86\91n] f.
 #n elim n -n //
 qed.