work in progress on frees_drops

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / relocation / lifts.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts.ma
index a621b819fb65603678c42c64bae4845f5c23e592..be42c0ebfa4d1742cd0bf70f57d2062b9dffa9b5 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts.ma
@@ -210,6 +210,28 @@ lemma lifts_inv_flat2: ∀f:rtmap. ∀I,V2,T2,X. ⬆*[f] X ≡ ⓕ{I}V2.T2 →
 
 (* Advanced inversion lemmas ************************************************)
 
+lemma lifts_inv_atom1: ∀f,I,Y. ⬆*[f] ⓪{I} ≡ Y →
+                       ∨∨ ∃∃s. I = Sort s & Y = ⋆s
+                        | ∃∃i,j. @⦃i, f⦄ ≡ j & I = LRef i & Y = #j
+                        | ∃∃l. I = GRef l & Y = §l.
+#f * #n #Y #H
+[ lapply (lifts_inv_sort1 … H)
+| elim (lifts_inv_lref1 … H)
+| lapply (lifts_inv_gref1 … H)
+] -H /3 width=5 by or3_intro0, or3_intro1, or3_intro2, ex3_2_intro, ex2_intro/
+qed-.
+
+lemma lifts_inv_atom2: ∀f,I,X. ⬆*[f] X ≡ ⓪{I} →
+                       ∨∨ ∃∃s. X = ⋆s & I = Sort s
+                        | ∃∃i,j. @⦃i, f⦄ ≡ j & X = #i & I = LRef j
+                        | ∃∃l. X = §l & I = GRef l.
+#f * #n #X #H
+[ lapply (lifts_inv_sort2 … H)
+| elim (lifts_inv_lref2 … H)
+| lapply (lifts_inv_gref2 … H)
+] -H /3 width=5 by or3_intro0, or3_intro1, or3_intro2, ex3_2_intro, ex2_intro/
+qed-.
+
 (* Basic_2A1: includes: lift_inv_pair_xy_x *)
 lemma lifts_inv_pair_xy_x: ∀f,I,V,T. ⬆*[f] ②{I}V.T ≡ V → ⊥.
 #f #J #V elim V -V
@@ -249,14 +271,6 @@ qed-.
 
 (* Basic forward lemmas *****************************************************)
 
-lemma lifts_fwd_atom2: ∀f,I,X. ⬆*[f] X ≡ ⓪{I} → ∃J. X = ⓪{J}. 
-#f * #n #X #H
-[ lapply (lifts_inv_sort2 … H)
-| elim (lifts_inv_lref2 … H)
-| lapply (lifts_inv_gref2 … H)
-] -H /2 width=2 by ex_intro/
-qed-.
-
 (* Basic_2A1: includes: lift_inv_O2 *)
 lemma lifts_fwd_isid: ∀f,T1,T2. ⬆*[f] T1 ≡ T2 → 𝐈⦃f⦄ → T1 = T2.
 #f #T1 #T2 #H elim H -f -T1 -T2