update in static_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / static / reqx_reqx.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/reqx_reqx.ma b/matita/matita/contribs/lambdadelta/static_2/static/reqx_reqx.ma
index f190e907ad4bfcc67189c394ca7dc650f87d798a..b6dc3d196b2cacee4373babb5767eca8164cac96 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/reqx_reqx.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/reqx_reqx.ma
@@ -12,37 +12,35 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "static_2/syntax/ext2_ext2.ma".
-include "static_2/syntax/teqx_teqx.ma".
-include "static_2/static/reqx_length.ma".
+include "static_2/static/reqg_reqg.ma".
+include "static_2/static/reqx.ma".
 
 (* SORT-IRRELEVANT EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ***)
 
 (* Advanced properties ******************************************************)
-
-(* Basic_2A1: uses: lleq_sym *)
+(*
 lemma reqx_sym: ∀T. symmetric … (reqx T).
 /3 width=3 by reqx_fsge_comp, rex_sym, teqx_sym/ qed-.
-
+*)
 (* Basic_2A1: uses: lleq_dec *)
-lemma reqx_dec: â\88\80L1,L2. â\88\80T:term. Decidable (L1 â\89\9b[T] L2).
-/3 width=1 by rex_dec, teqx_dec/ qed-.
-
+lemma reqx_dec: â\88\80L1,L2. â\88\80T:term. Decidable (L1 â\89\85[T] L2).
+/2 width=1 by reqg_dec/ qed-.
+(*
 (* Main properties **********************************************************)
 
-(* Basic_2A1: uses: lleq_bind lleq_bind_O *) 
+(* Basic_2A1: uses: lleq_bind lleq_bind_O *)
 theorem reqx_bind: ∀p,I,L1,L2,V1,V2,T.
-                   L1 ≛[V1] L2 → L1.ⓑ{I}V1 ≛[T] L2.ⓑ{I}V2 →
-                   L1 ≛[ⓑ{p,I}V1.T] L2.
+                   L1 ≛[V1] L2 → L1.ⓑ[I]V1 ≛[T] L2.ⓑ[I]V2 →
+                   L1 ≛[ⓑ[p,I]V1.T] L2.
 /2 width=2 by rex_bind/ qed.
 
 (* Basic_2A1: uses: lleq_flat *)
 theorem reqx_flat: ∀I,L1,L2,V,T.
-                   L1 ≛[V] L2 → L1 ≛[T] L2 → L1 ≛[ⓕ{I}V.T] L2.
+                   L1 ≛[V] L2 → L1 ≛[T] L2 → L1 ≛[ⓕ[I]V.T] L2.
 /2 width=1 by rex_flat/ qed.
 
 theorem reqx_bind_void: ∀p,I,L1,L2,V,T.
-                        L1 ≛[V] L2 → L1.ⓧ ≛[T] L2.ⓧ → L1 ≛[ⓑ{p,I}V.T] L2.
+                        L1 ≛[V] L2 → L1.ⓧ ≛[T] L2.ⓧ → L1 ≛[ⓑ[p,I]V.T] L2.
 /2 width=1 by rex_bind_void/ qed.
 
 (* Basic_2A1: uses: lleq_trans *)
@@ -61,13 +59,13 @@ theorem reqx_canc_sn: ∀T. left_cancellable … (reqx T).
 theorem reqx_canc_dx: ∀T. right_cancellable … (reqx T).
 /3 width=3 by reqx_trans, reqx_sym/ qed-.
 
-theorem reqx_repl: â\88\80L1,L2. â\88\80T:term. L1 â\89\9b[T] L2 →
-                   â\88\80K1. L1 â\89\9b[T] K1 â\86\92 â\88\80K2. L2 â\89\9b[T] K2 â\86\92 K1 â\89\9b[T] K2.
-/3 width=3 by reqx_canc_sn, reqx_trans/ qed-.
+theorem reqx_repl: â\88\80L1,L2. â\88\80T:term. L1 â\89\85[T] L2 →
+                   â\88\80K1. L1 â\89\85[T] K1 â\86\92 â\88\80K2. L2 â\89\85[T] K2 â\86\92 K1 â\89\85[T] K2.
+/2 width=5 by reqg_repl/ qed-.
 
 (* Negated properties *******************************************************)
 
-(* Note: auto works with /4 width=8/ so reqx_canc_sn is preferred **********) 
+(* Note: auto works with /4 width=8/ so reqx_canc_sn is preferred **********)
 (* Basic_2A1: uses: lleq_nlleq_trans *)
 lemma reqx_rneqx_trans: ∀T:term.∀L1,L. L1 ≛[T] L →
                         ∀L2. (L ≛[T] L2 → ⊥) → (L1 ≛[T] L2 → ⊥).
@@ -85,15 +83,16 @@ theorem rneqx_reqx_canc_dx: ∀L1,L. ∀T:term. (L1 ≛[T] L → ⊥) →
 (* Negated inversion lemmas *************************************************)
 
 (* Basic_2A1: uses: nlleq_inv_bind nlleq_inv_bind_O *)
-lemma rneqx_inv_bind: ∀p,I,L1,L2,V,T. (L1 ≛[ⓑ{p,I}V.T] L2 → ⊥) →
-                      (L1 ≛[V] L2 → ⊥) ∨ (L1.ⓑ{I}V ≛[T] L2.ⓑ{I}V → ⊥).
+lemma rneqx_inv_bind: ∀p,I,L1,L2,V,T. (L1 ≛[ⓑ[p,I]V.T] L2 → ⊥) →
+                      (L1 ≛[V] L2 → ⊥) ∨ (L1.ⓑ[I]V ≛[T] L2.ⓑ[I]V → ⊥).
 /3 width=2 by rnex_inv_bind, teqx_dec/ qed-.
 
 (* Basic_2A1: uses: nlleq_inv_flat *)
-lemma rneqx_inv_flat: ∀I,L1,L2,V,T. (L1 ≛[ⓕ{I}V.T] L2 → ⊥) →
+lemma rneqx_inv_flat: ∀I,L1,L2,V,T. (L1 ≛[ⓕ[I]V.T] L2 → ⊥) →
                       (L1 ≛[V] L2 → ⊥) ∨ (L1 ≛[T] L2 → ⊥).
 /3 width=2 by rnex_inv_flat, teqx_dec/ qed-.
 
-lemma rneqx_inv_bind_void: ∀p,I,L1,L2,V,T. (L1 ≛[ⓑ{p,I}V.T] L2 → ⊥) →
+lemma rneqx_inv_bind_void: ∀p,I,L1,L2,V,T. (L1 ≛[ⓑ[p,I]V.T] L2 → ⊥) →
                            (L1 ≛[V] L2 → ⊥) ∨ (L1.ⓧ ≛[T] L2.ⓧ → ⊥).
 /3 width=3 by rnex_inv_bind_void, teqx_dec/ qed-.
+*)