X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fstatic_2%2Fstatic%2Frex_rex.ma;h=10d2b917818dfc203f18690de3a75206fd1a4a17;hp=7bbf5d895c78ec40deb9590ef4258c52b38ae4d9;hb=a454837a256907d2f83d42ced7be847e10361ea9;hpb=b4283c079ed7069016b8d924bbc7e08872440829

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/rex_rex.ma b/matita/matita/contribs/lambdadelta/static_2/static/rex_rex.ma
index 7bbf5d895..10d2b9178 100644
--- a/matita/matita/contribs/lambdadelta/static_2/static/rex_rex.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/rex_rex.ma
@@ -20,16 +20,18 @@ include "static_2/static/rex.ma".
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma rex_inv_frees: ∀R,L1,L2,T. L1 ⪤[R,T] L2 →
-                     ∀f. L1 ⊢ 𝐅*⦃T⦄ ≘ f → L1 ⪤[cext2 R,cfull,f] L2.
+lemma rex_inv_frees (R):
+      ∀L1,L2,T. L1 ⪤[R,T] L2 →
+      ∀f. L1 ⊢ 𝐅+⦃T⦄ ≘ f → L1 ⪤[cext2 R,cfull,f] L2.
 #R #L1 #L2 #T * /3 width=6 by frees_mono, sex_eq_repl_back/
 qed-.
 
 (* Advanced properties ******************************************************)
 
 (* Basic_2A1: uses: llpx_sn_dec *)
-lemma rex_dec: ∀R. (∀L,T1,T2. Decidable (R L T1 T2)) →
-               ∀L1,L2,T. Decidable (L1 ⪤[R,T] L2).
+lemma rex_dec (R):
+      (∀L,T1,T2. Decidable (R L T1 T2)) →
+      ∀L1,L2,T. Decidable (L1 ⪤[R,T] L2).
 #R #HR #L1 #L2 #T
 elim (frees_total L1 T) #f #Hf
 elim (sex_dec (cext2 R) cfull … L1 L2 f)
@@ -39,25 +41,23 @@ qed-.
 (* Main properties **********************************************************)
 
 (* Basic_2A1: uses: llpx_sn_bind llpx_sn_bind_O *)
-theorem rex_bind: ∀R,p,I,L1,L2,V1,V2,T.
-                  L1 ⪤[R,V1] L2 → L1.ⓑ{I}V1 ⪤[R,T] L2.ⓑ{I}V2 →
-                  L1 ⪤[R,ⓑ{p,I}V1.T] L2.
+theorem rex_bind (R) (p) (I):
+        ∀L1,L2,V1,V2,T. L1 ⪤[R,V1] L2 → L1.ⓑ{I}V1 ⪤[R,T] L2.ⓑ{I}V2 →
+        L1 ⪤[R,ⓑ{p,I}V1.T] L2.
 #R #p #I #L1 #L2 #V1 #V2 #T * #f1 #HV #Hf1 * #f2 #HT #Hf2
 lapply (sex_fwd_bind … Hf2) -Hf2 #Hf2 elim (sor_isfin_ex f1 (⫱f2))
 /3 width=7 by frees_fwd_isfin, frees_bind, sex_join, isfin_tl, ex2_intro/
 qed.
 
 (* Basic_2A1: llpx_sn_flat *)
-theorem rex_flat: ∀R,I,L1,L2,V,T.
-                  L1 ⪤[R,V] L2 → L1 ⪤[R,T] L2 →
-                  L1 ⪤[R,ⓕ{I}V.T] L2.
+theorem rex_flat (R) (I):
+        ∀L1,L2,V,T. L1 ⪤[R,V] L2 → L1 ⪤[R,T] L2 → L1 ⪤[R,ⓕ{I}V.T] L2.
 #R #I #L1 #L2 #V #T * #f1 #HV #Hf1 * #f2 #HT #Hf2 elim (sor_isfin_ex f1 f2)
 /3 width=7 by frees_fwd_isfin, frees_flat, sex_join, ex2_intro/
 qed.
 
-theorem rex_bind_void: ∀R,p,I,L1,L2,V,T.
-                       L1 ⪤[R,V] L2 → L1.ⓧ ⪤[R,T] L2.ⓧ →
-                       L1 ⪤[R,ⓑ{p,I}V.T] L2.
+theorem rex_bind_void (R) (p) (I):
+        ∀L1,L2,V,T. L1 ⪤[R,V] L2 → L1.ⓧ ⪤[R,T] L2.ⓧ → L1 ⪤[R,ⓑ{p,I}V.T] L2.
 #R #p #I #L1 #L2 #V #T * #f1 #HV #Hf1 * #f2 #HT #Hf2
 lapply (sex_fwd_bind … Hf2) -Hf2 #Hf2 elim (sor_isfin_ex f1 (⫱f2))
 /3 width=7 by frees_fwd_isfin, frees_bind_void, sex_join, isfin_tl, ex2_intro/
@@ -66,24 +66,27 @@ qed.
 (* Negated inversion lemmas *************************************************)
 
 (* Basic_2A1: uses: nllpx_sn_inv_bind nllpx_sn_inv_bind_O *)
-lemma rnex_inv_bind: ∀R. (∀L,T1,T2. Decidable (R L T1 T2)) →
-                     ∀p,I,L1,L2,V,T. (L1 ⪤[R,ⓑ{p,I}V.T] L2 → ⊥) →
-                     (L1 ⪤[R,V] L2 → ⊥) ∨ (L1.ⓑ{I}V ⪤[R,T] L2.ⓑ{I}V → ⊥).
+lemma rnex_inv_bind (R):
+      (∀L,T1,T2. Decidable (R L T1 T2)) →
+      ∀p,I,L1,L2,V,T. (L1 ⪤[R,ⓑ{p,I}V.T] L2 → ⊥) →
+      ∨∨ (L1 ⪤[R,V] L2 → ⊥) | (L1.ⓑ{I}V ⪤[R,T] L2.ⓑ{I}V → ⊥).
 #R #HR #p #I #L1 #L2 #V #T #H elim (rex_dec … HR L1 L2 V)
 /4 width=2 by rex_bind, or_intror, or_introl/
 qed-.
 
 (* Basic_2A1: uses: nllpx_sn_inv_flat *)
-lemma rnex_inv_flat: ∀R. (∀L,T1,T2. Decidable (R L T1 T2)) →
-                     ∀I,L1,L2,V,T. (L1 ⪤[R,ⓕ{I}V.T] L2 → ⊥) →
-                     (L1 ⪤[R,V] L2 → ⊥) ∨ (L1 ⪤[R,T] L2 → ⊥).
+lemma rnex_inv_flat (R):
+      (∀L,T1,T2. Decidable (R L T1 T2)) →
+      ∀I,L1,L2,V,T. (L1 ⪤[R,ⓕ{I}V.T] L2 → ⊥) →
+      ∨∨ (L1 ⪤[R,V] L2 → ⊥) | (L1 ⪤[R,T] L2 → ⊥).
 #R #HR #I #L1 #L2 #V #T #H elim (rex_dec … HR L1 L2 V)
 /4 width=1 by rex_flat, or_intror, or_introl/
 qed-.
 
-lemma rnex_inv_bind_void: ∀R. (∀L,T1,T2. Decidable (R L T1 T2)) →
-                          ∀p,I,L1,L2,V,T. (L1 ⪤[R,ⓑ{p,I}V.T] L2 → ⊥) →
-                          (L1 ⪤[R,V] L2 → ⊥) ∨ (L1.ⓧ ⪤[R,T] L2.ⓧ → ⊥).
+lemma rnex_inv_bind_void (R):
+      (∀L,T1,T2. Decidable (R L T1 T2)) →
+      ∀p,I,L1,L2,V,T. (L1 ⪤[R,ⓑ{p,I}V.T] L2 → ⊥) →
+      ∨∨ (L1 ⪤[R,V] L2 → ⊥) | (L1.ⓧ ⪤[R,T] L2.ⓧ → ⊥).
 #R #HR #p #I #L1 #L2 #V #T #H elim (rex_dec … HR L1 L2 V)
 /4 width=2 by rex_bind_void, or_intror, or_introl/
 qed-.