update in staic_2 and basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/req.ma b/matita/matita/contribs/lambdadelta/static_2/static/req.ma
index fcd79b33a68ddf9c8068ef631fe95d0da61993e4..b53ef17559be823ba437c3a92daf35dad4cd9c8c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/req.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/req.ma
@@ -19,65 +19,73 @@ include "static_2/static/rex.ma".
 
 (* Basic_2A1: was: lleq *)
 definition req: relation3 term lenv lenv ≝
-                rex ceq.
+           rex ceq.
 
 interpretation
-   "syntactic equivalence on referred entries (local environment)"
-   'IdEqSn T L1 L2 = (req T L1 L2).
+  "syntactic equivalence on referred entries (local environment)"
+  'IdEqSn T L1 L2 = (req T L1 L2).
 
-(* Note: "req_transitive R" is equivalent to "rex_transitive ceq R R" *)
+(* Note: "R_transitive_req R" is equivalent to "R_transitive_rex ceq R R" *)
 (* Basic_2A1: uses: lleq_transitive *)
-definition req_transitive: predicate (relation3 lenv term term) ≝
+definition R_transitive_req: predicate (relation3 lenv term term) ≝
            λR. ∀L2,T1,T2. R L2 T1 T2 → ∀L1. L1 ≡[T1] L2 → R L1 T1 T2.
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma req_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 req_inv_bind:
+      ∀p,I,L1,L2,V,T. L1 ≡[ⓑ[p,I]V.T] L2 →
+      ∧∧ L1 ≡[V] L2 & L1.ⓑ[I]V ≡[T] L2.ⓑ[I]V.
 /2 width=2 by rex_inv_bind/ qed-.
 
-lemma req_inv_flat: ∀I,L1,L2,V,T. L1 ≡[ⓕ[I]V.T] L2 →
-                    ∧∧ L1 ≡[V] L2 & L1 ≡[T] L2.
+lemma req_inv_flat:
+      ∀I,L1,L2,V,T. L1 ≡[ⓕ[I]V.T] L2 →
+      ∧∧ L1 ≡[V] L2 & L1 ≡[T] L2.
 /2 width=2 by rex_inv_flat/ qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma req_inv_zero_pair_sn: ∀I,L2,K1,V. K1.ⓑ[I]V ≡[#0] L2 →
-                            ∃∃K2. K1 ≡[V] K2 & L2 = K2.ⓑ[I]V.
+lemma req_inv_zero_pair_sn:
+      ∀I,L2,K1,V. K1.ⓑ[I]V ≡[#0] L2 →
+      ∃∃K2. K1 ≡[V] K2 & L2 = K2.ⓑ[I]V.
 #I #L2 #K1 #V #H
 elim (rex_inv_zero_pair_sn … H) -H #K2 #X #HK12 #HX #H destruct
 /2 width=3 by ex2_intro/
 qed-.
 
-lemma req_inv_zero_pair_dx: ∀I,L1,K2,V. L1 ≡[#0] K2.ⓑ[I]V →
-                            ∃∃K1. K1 ≡[V] K2 & L1 = K1.ⓑ[I]V.
+lemma req_inv_zero_pair_dx:
+      ∀I,L1,K2,V. L1 ≡[#0] K2.ⓑ[I]V →
+      ∃∃K1. K1 ≡[V] K2 & L1 = K1.ⓑ[I]V.
 #I #L1 #K2 #V #H
 elim (rex_inv_zero_pair_dx … H) -H #K1 #X #HK12 #HX #H destruct
 /2 width=3 by ex2_intro/
 qed-.
 
-lemma req_inv_lref_bind_sn: ∀I1,K1,L2,i. K1.ⓘ[I1] ≡[#↑i] L2 →
-                            ∃∃I2,K2. K1 ≡[#i] K2 & L2 = K2.ⓘ[I2].
+lemma req_inv_lref_bind_sn:
+      ∀I1,K1,L2,i. K1.ⓘ[I1] ≡[#↑i] L2 →
+      ∃∃I2,K2. K1 ≡[#i] K2 & L2 = K2.ⓘ[I2].
 /2 width=2 by rex_inv_lref_bind_sn/ qed-.
 
-lemma req_inv_lref_bind_dx: ∀I2,K2,L1,i. L1 ≡[#↑i] K2.ⓘ[I2] →
-                            ∃∃I1,K1. K1 ≡[#i] K2 & L1 = K1.ⓘ[I1].
+lemma req_inv_lref_bind_dx:
+      ∀I2,K2,L1,i. L1 ≡[#↑i] K2.ⓘ[I2] →
+      ∃∃I1,K1. K1 ≡[#i] K2 & L1 = K1.ⓘ[I1].
 /2 width=2 by rex_inv_lref_bind_dx/ qed-.
 
 (* Basic forward lemmas *****************************************************)
 
 (* Basic_2A1: was: llpx_sn_lrefl *)
 (* Basic_2A1: this should have been lleq_fwd_llpx_sn *)
-lemma req_fwd_rex: ∀R. c_reflexive … R →
-                   ∀L1,L2,T. L1 ≡[T] L2 → L1 ⪤[R,T] L2.
+lemma req_fwd_rex (R):
+      c_reflexive … R →
+      ∀L1,L2,T. L1 ≡[T] L2 → L1 ⪤[R,T] L2.
 #R #HR #L1 #L2 #T * #f #Hf #HL12
 /4 width=7 by sex_co, cext2_co, ex2_intro/
 qed-.
 
 (* Basic_properties *********************************************************)
 
-lemma frees_req_conf: ∀f,L1,T. L1 ⊢ 𝐅+❪T❫ ≘ f →
-                      ∀L2. L1 ≡[T] L2 → L2 ⊢ 𝐅+❪T❫ ≘ f.
+lemma frees_req_conf:
+      ∀f,L1,T. L1 ⊢ 𝐅+❪T❫ ≘ f →
+      ∀L2. L1 ≡[T] L2 → L2 ⊢ 𝐅+❪T❫ ≘ f.
 #f #L1 #T #H elim H -f -L1 -T
 [ /2 width=3 by frees_sort/
 | #f #i #Hf #L2 #H2