update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / lfpx_length.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_length.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_length.ma
index d0ca2b90c34a0c028d3da78e788779cde3c4f1a7..7b194bd71555d668d08e433494773fff846ab9b1 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_length.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_length.ma
@@ -22,3 +22,13 @@ include "basic_2/rt_transition/lfpx.ma".
 (* Basic_2A1: uses: lpx_fwd_length *)
 lemma lfpx_fwd_length: ∀h,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈[h, T] L2 → |L1| = |L2|.
 /2 width=3 by lfxs_fwd_length/ qed-.
+
+(* Inversion lemmas with length for local environments **********************)
+
+lemma lfpx_inv_zero_length: ∀h,G,Y1,Y2. ⦃G, Y1⦄ ⊢ ⬈[h, #0] Y2 →
+                            ∨∨ ∧∧ Y1 = ⋆ & Y2 = ⋆
+                             | ∃∃I,L1,L2,V1,V2. ⦃G, L1⦄ ⊢ ⬈[h, V1] L2 &
+                                                ⦃G, L1⦄ ⊢ V1 ⬈[h] V2 &
+                                                Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2
+                             |∃∃I,L1,L2. |L1| = |L2| & Y1 = L1.ⓤ{I} & Y2 = L2.ⓤ{I}.
+/2 width=1 by lfxs_inv_zero_length/ qed-.