- notation change for tdeq and related notions

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / lfsx_lfpxs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_lfpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_lfpxs.ma
index 31a027834c09f98cec0a489ff49c060591863458..23250e0f6565c36c0db5a40c431b7fa072a876a7 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_lfpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_lfpxs.ma
@@ -23,7 +23,7 @@ include "basic_2/rt_computation/lfsx_lfsx.ma".
 
 (* Basic_2A1: uses: lsx_intro_alt *)
 lemma lfsx_intro_lfpxs: ∀h,o,G,L1,T.
-                        (â\88\80L2. â¦\83G, L1â¦\84 â\8a¢ â¬\88*[h, T] L2 â\86\92 (L1 â\89¡[h, o, T] L2 → ⊥) → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄) →
+                        (â\88\80L2. â¦\83G, L1â¦\84 â\8a¢ â¬\88*[h, T] L2 â\86\92 (L1 â\89\9b[h, o, T] L2 → ⊥) → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄) →
                         G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄.
 /4 width=1 by lfpx_lfpxs, lfsx_intro/ qed-.
 
@@ -38,11 +38,11 @@ qed-.
 
 lemma lfsx_ind_lfpxs_lfdeq: ∀h,o,G,T. ∀R:predicate lenv.
                             (∀L1. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄ →
-                                  (â\88\80L2. â¦\83G, L1â¦\84 â\8a¢ â¬\88*[h, T] L2 â\86\92 (L1 â\89¡[h, o, T] L2 → ⊥) → R L2) →
+                                  (â\88\80L2. â¦\83G, L1â¦\84 â\8a¢ â¬\88*[h, T] L2 â\86\92 (L1 â\89\9b[h, o, T] L2 → ⊥) → R L2) →
                                   R L1
                             ) →
                             ∀L1. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄  →
-                            â\88\80L0. â¦\83G, L1â¦\84 â\8a¢ â¬\88*[h, T] L0 â\86\92 â\88\80L2. L0 â\89¡[h, o, T] L2 → R L2.
+                            â\88\80L0. â¦\83G, L1â¦\84 â\8a¢ â¬\88*[h, T] L0 â\86\92 â\88\80L2. L0 â\89\9b[h, o, T] L2 → R L2.
 #h #o #G #T #R #IH #L1 #H @(lfsx_ind … H) -L1
 #L1 #HL1 #IH1 #L0 #HL10 #L2 #HL02
 @IH -IH /3 width=3 by lfsx_lfpxs_trans, lfsx_lfdeq_trans/ -HL1 #K2 #HLK2 #HnLK2
@@ -63,7 +63,7 @@ qed-.
 (* Basic_2A1: uses: lsx_ind_alt *)
 lemma lfsx_ind_lfpxs: ∀h,o,G,T. ∀R:predicate lenv.
                       (∀L1. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄ →
-                            (â\88\80L2. â¦\83G, L1â¦\84 â\8a¢ â¬\88*[h, T] L2 â\86\92 (L1 â\89¡[h, o, T] L2 → ⊥) → R L2) →
+                            (â\88\80L2. â¦\83G, L1â¦\84 â\8a¢ â¬\88*[h, T] L2 â\86\92 (L1 â\89\9b[h, o, T] L2 → ⊥) → R L2) →
                             R L1
                       ) →
                       ∀L. G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄  → R L.
@@ -120,3 +120,27 @@ qed-.
 lemma lfsx_flat: ∀h,o,I,G,L,V. G ⊢ ⬈*[h, o, V] 𝐒⦃L⦄ →
                  ∀T. G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄ → G ⊢ ⬈*[h, o, ⓕ{I}V.T] 𝐒⦃L⦄.
 /2 width=3 by lfsx_flat_lfpxs/ qed.
+
+fact lfsx_bind_lfpxs_void_aux: ∀h,o,p,I,G,L1,V. G ⊢ ⬈*[h, o, V] 𝐒⦃L1⦄ →
+                               ∀Y,T. G ⊢ ⬈*[h, o, T] 𝐒⦃Y⦄ →
+                               ∀L2. Y = L2.ⓧ → ⦃G, L1⦄ ⊢ ⬈*[h, ⓑ{p,I}V.T] L2 →
+                               G ⊢ ⬈*[h, o, ⓑ{p,I}V.T] 𝐒⦃L2⦄.
+#h #o #p #I #G #L1 #V #H @(lfsx_ind_lfpxs … H) -L1
+#L1 #_ #IHL1 #Y #T #H @(lfsx_ind_lfpxs … H) -Y
+#Y #HY #IHY #L2 #H #HL12 destruct
+@lfsx_intro_lfpxs #L0 #HL20
+lapply (lfpxs_trans … HL12 … HL20) #HL10 #H
+elim (lfdneq_inv_bind_void … H) -H [ -IHY | -HY -IHL1 -HL12 ]
+[ #HnV elim (lfdeq_dec h o L1 L2 V)
+  [ #HV @(IHL1 … L0) -IHL1 -HL12
+    /3 width=6 by lfsx_lfpxs_trans, lfpxs_fwd_bind_dx_void, lfpxs_fwd_pair_sn, lfdeq_canc_sn/ (**) (* full auto too slow *)
+  | -HnV -HL10 /4 width=4 by lfsx_lfpxs_trans, lfpxs_fwd_pair_sn/
+  ]
+| /3 width=4 by lfpxs_fwd_bind_dx_void/
+]
+qed-.
+
+lemma lfsx_bind_void: ∀h,o,p,I,G,L,V. G ⊢ ⬈*[h, o, V] 𝐒⦃L⦄ →
+                      ∀T. G ⊢ ⬈*[h, o, T] 𝐒⦃L.ⓧ⦄ →
+                      G ⊢ ⬈*[h, o, ⓑ{p,I}V.T] 𝐒⦃L⦄.
+/2 width=3 by lfsx_bind_lfpxs_void_aux/ qed.