milestone in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/rdeq_rdeq.ma b/matita/matita/contribs/lambdadelta/static_2/static/rdeq_rdeq.ma
index 316438d662241b1c5a9325fa866db8ff9ff78d34..30069162df6bb1575ab1056b90558ec858b7eb37 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/rdeq_rdeq.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/rdeq_rdeq.ma
@@ -16,85 +16,84 @@ include "static_2/syntax/ext2_ext2.ma".
 include "static_2/syntax/tdeq_tdeq.ma".
 include "static_2/static/rdeq_length.ma".
 
-(* DEGREE-BASED EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ******)
+(* SORT-IRRELEVANT EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ***)
 
 (* Advanced properties ******************************************************)
 
 (* Basic_2A1: uses: lleq_sym *)
-lemma rdeq_sym: ∀h,o,T. symmetric … (rdeq h o T).
+lemma rdeq_sym: ∀T. symmetric … (rdeq T).
 /3 width=3 by rdeq_fsge_comp, rex_sym, tdeq_sym/ qed-.
 
 (* Basic_2A1: uses: lleq_dec *)
-lemma rdeq_dec: ∀h,o,L1,L2. ∀T:term. Decidable (L1 ≛[h, o, T] L2).
+lemma rdeq_dec: ∀L1,L2. ∀T:term. Decidable (L1 ≛[T] L2).
 /3 width=1 by rex_dec, tdeq_dec/ qed-.
 
 (* Main properties **********************************************************)
 
 (* Basic_2A1: uses: lleq_bind lleq_bind_O *) 
-theorem rdeq_bind: ∀h,o,p,I,L1,L2,V1,V2,T.
-                   L1 ≛[h, o, V1] L2 → L1.ⓑ{I}V1 ≛[h, o, T] L2.ⓑ{I}V2 →
-                   L1 ≛[h, o, ⓑ{p,I}V1.T] L2.
+theorem rdeq_bind: ∀p,I,L1,L2,V1,V2,T.
+                   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 rdeq_flat: ∀h,o,I,L1,L2,V,T. L1 ≛[h, o, V] L2 → L1 ≛[h, o, T] L2 →
-                   L1 ≛[h, o, ⓕ{I}V.T] L2.
+theorem rdeq_flat: ∀I,L1,L2,V,T.
+                   L1 ≛[V] L2 → L1 ≛[T] L2 → L1 ≛[ⓕ{I}V.T] L2.
 /2 width=1 by rex_flat/ qed.
 
-theorem rdeq_bind_void: ∀h,o,p,I,L1,L2,V,T.
-                        L1 ≛[h, o, V] L2 → L1.ⓧ ≛[h, o, T] L2.ⓧ →
-                        L1 ≛[h, o, ⓑ{p,I}V.T] L2.
+theorem rdeq_bind_void: ∀p,I,L1,L2,V,T.
+                        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 *)
-theorem rdeq_trans: ∀h,o,T. Transitive … (rdeq h o T).
-#h #o #T #L1 #L * #f1 #Hf1 #HL1 #L2 * #f2 #Hf2 #HL2
+theorem rdeq_trans: ∀T. Transitive … (rdeq T).
+#T #L1 #L * #f1 #Hf1 #HL1 #L2 * #f2 #Hf2 #HL2
 lapply (frees_tdeq_conf_rdeq … Hf1 T … HL1) // #H0
 lapply (frees_mono … Hf2 … H0) -Hf2 -H0
 /5 width=7 by sex_trans, sex_eq_repl_back, tdeq_trans, ext2_trans, ex2_intro/
 qed-.
 
 (* Basic_2A1: uses: lleq_canc_sn *)
-theorem rdeq_canc_sn: ∀h,o,T. left_cancellable … (rdeq h o T).
+theorem rdeq_canc_sn: ∀T. left_cancellable … (rdeq T).
 /3 width=3 by rdeq_trans, rdeq_sym/ qed-.
 
 (* Basic_2A1: uses: lleq_canc_dx *)
-theorem rdeq_canc_dx: ∀h,o,T. right_cancellable … (rdeq h o T).
+theorem rdeq_canc_dx: ∀T. right_cancellable … (rdeq T).
 /3 width=3 by rdeq_trans, rdeq_sym/ qed-.
 
-theorem rdeq_repl: ∀h,o,L1,L2. ∀T:term. L1 ≛[h, o, T] L2 →
-                   ∀K1. L1 ≛[h, o, T] K1 → ∀K2. L2 ≛[h, o, T] K2 → K1 ≛[h, o, T] K2.
+theorem rdeq_repl: ∀L1,L2. ∀T:term. L1 ≛[T] L2 →
+                   ∀K1. L1 ≛[T] K1 → ∀K2. L2 ≛[T] K2 → K1 ≛[T] K2.
 /3 width=3 by rdeq_canc_sn, rdeq_trans/ qed-.
 
 (* Negated properties *******************************************************)
 
 (* Note: auto works with /4 width=8/ so rdeq_canc_sn is preferred **********) 
 (* Basic_2A1: uses: lleq_nlleq_trans *)
-lemma rdeq_rdneq_trans: ∀h,o.∀T:term.∀L1,L. L1 ≛[h, o, T] L →
-                        ∀L2. (L ≛[h, o, T] L2 → ⊥) → (L1 ≛[h, o, T] L2 → ⊥).
+lemma rdeq_rdneq_trans: ∀T:term.∀L1,L. L1 ≛[T] L →
+                        ∀L2. (L ≛[T] L2 → ⊥) → (L1 ≛[T] L2 → ⊥).
 /3 width=3 by rdeq_canc_sn/ qed-.
 
 (* Basic_2A1: uses: nlleq_lleq_div *)
-lemma rdneq_rdeq_div: ∀h,o.∀T:term.∀L2,L. L2 ≛[h, o, T] L →
-                      ∀L1. (L1 ≛[h, o, T] L → ⊥) → (L1 ≛[h, o, T] L2 → ⊥).
+lemma rdneq_rdeq_div: ∀T:term.∀L2,L. L2 ≛[T] L →
+                      ∀L1. (L1 ≛[T] L → ⊥) → (L1 ≛[T] L2 → ⊥).
 /3 width=3 by rdeq_trans/ qed-.
 
-theorem rdneq_rdeq_canc_dx: ∀h,o,L1,L. ∀T:term. (L1 ≛[h, o, T] L → ⊥) →
-                            ∀L2. L2 ≛[h, o, T] L → L1 ≛[h, o, T] L2 → ⊥.
+theorem rdneq_rdeq_canc_dx: ∀L1,L. ∀T:term. (L1 ≛[T] L → ⊥) →
+                            ∀L2. L2 ≛[T] L → L1 ≛[T] L2 → ⊥.
 /3 width=3 by rdeq_trans/ qed-.
 
 (* Negated inversion lemmas *************************************************)
 
 (* Basic_2A1: uses: nlleq_inv_bind nlleq_inv_bind_O *)
-lemma rdneq_inv_bind: ∀h,o,p,I,L1,L2,V,T. (L1 ≛[h, o, ⓑ{p,I}V.T] L2 → ⊥) →
-                      (L1 ≛[h, o, V] L2 → ⊥) ∨ (L1.ⓑ{I}V ≛[h, o, T] L2.ⓑ{I}V → ⊥).
+lemma rdneq_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, tdeq_dec/ qed-.
 
 (* Basic_2A1: uses: nlleq_inv_flat *)
-lemma rdneq_inv_flat: ∀h,o,I,L1,L2,V,T. (L1 ≛[h, o, ⓕ{I}V.T] L2 → ⊥) →
-                      (L1 ≛[h, o, V] L2 → ⊥) ∨ (L1 ≛[h, o, T] L2 → ⊥).
+lemma rdneq_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, tdeq_dec/ qed-.
 
-lemma rdneq_inv_bind_void: ∀h,o,p,I,L1,L2,V,T. (L1 ≛[h, o, ⓑ{p,I}V.T] L2 → ⊥) →
-                           (L1 ≛[h, o, V] L2 → ⊥) ∨ (L1.ⓧ ≛[h, o, T] L2.ⓧ → ⊥).
+lemma rdneq_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, tdeq_dec/ qed-.