X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Freduction%2Fcrr.ma;h=9158a53af5dc1dc92f6ef1354d17075a2658e67d;hb=a76f56fdad6348b167376093920650379c9936d4;hp=01ed1dbabc8b31873ef939c2cacd1c9232ebe9ef;hpb=8ed01fd6a38bea715ceb449bb7b72a46bad87851;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/crr.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/crr.ma
index 01ed1dbab..9158a53af 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/crr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/crr.ma
@@ -12,11 +12,11 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/reducible_3.ma".
+include "basic_2/notation/relations/predreducible_3.ma".
 include "basic_2/grammar/genv.ma".
 include "basic_2/relocation/ldrop.ma".
 
-(* CONTEXT-SENSITIVE REDUCIBLE TERMS ****************************************)
+(* REDUCIBLE TERMS FOR CONTEXT-SENSITIVE REDUCTION **************************)
 
 (* reducible binary items *)
 definition ri2: predicate item2 ≝
@@ -29,7 +29,7 @@ definition ib2: relation2 bool bind2 ≝
 (* activate genv *)
 (* reducible terms *)
 inductive crr (G:genv): relation2 lenv term ≝
-| crr_delta  : ∀L,K,V,i. ⇩[0, i] L ≡ K.ⓓV → crr G L (#i)
+| crr_delta  : ∀L,K,V,i. ⇩[i] L ≡ K.ⓓV → crr G L (#i)
 | crr_appl_sn: ∀L,V,T. crr G L V → crr G L (ⓐV.T)
 | crr_appl_dx: ∀L,V,T. crr G L T → crr G L (ⓐV.T)
 | crr_ri2    : ∀I,L,V,T. ri2 I → crr G L (②{I}V.T)
@@ -40,12 +40,12 @@ inductive crr (G:genv): relation2 lenv term ≝
 .
 
 interpretation
-   "context-sensitive reducibility (term)"
-   'Reducible G L T = (crr G L T).
+   "reducibility for context-sensitive reduction (term)"
+   'PRedReducible G L T = (crr G L T).
 
 (* Basic inversion lemmas ***************************************************)
 
-fact crr_inv_sort_aux: ∀G,L,T,k. ⦃G, L⦄ ⊢ 𝐑⦃T⦄ → T = ⋆k → ⊥.
+fact crr_inv_sort_aux: ∀G,L,T,k. ⦃G, L⦄ ⊢ ➡ 𝐑⦃T⦄ → T = ⋆k → ⊥.
 #G #L #T #k0 * -L -T
 [ #L #K #V #i #HLK #H destruct
 | #L #V #T #_ #H destruct
@@ -58,13 +58,13 @@ fact crr_inv_sort_aux: ∀G,L,T,k. ⦃G, L⦄ ⊢ 𝐑⦃T⦄ → T = ⋆k → 
 ]
 qed-.
 
-lemma crr_inv_sort: ∀G,L,k. ⦃G, L⦄ ⊢ 𝐑⦃⋆k⦄ → ⊥.
+lemma crr_inv_sort: ∀G,L,k. ⦃G, L⦄ ⊢ ➡ 𝐑⦃⋆k⦄ → ⊥.
 /2 width=6 by crr_inv_sort_aux/ qed-.
 
-fact crr_inv_lref_aux: ∀G,L,T,i. ⦃G, L⦄ ⊢ 𝐑⦃T⦄ → T = #i →
-                       ∃∃K,V. ⇩[0, i] L ≡ K.ⓓV.
+fact crr_inv_lref_aux: ∀G,L,T,i. ⦃G, L⦄ ⊢ ➡ 𝐑⦃T⦄ → T = #i →
+                       ∃∃K,V. ⇩[i] L ≡ K.ⓓV.
 #G #L #T #j * -L -T
-[ #L #K #V #i #HLK #H destruct /2 width=3/
+[ #L #K #V #i #HLK #H destruct /2 width=3 by ex1_2_intro/
 | #L #V #T #_ #H destruct
 | #L #V #T #_ #H destruct
 | #I #L #V #T #_ #H destruct
@@ -75,10 +75,10 @@ fact crr_inv_lref_aux: ∀G,L,T,i. ⦃G, L⦄ ⊢ 𝐑⦃T⦄ → T = #i →
 ]
 qed-.
 
-lemma crr_inv_lref: ∀G,L,i. ⦃G, L⦄ ⊢ 𝐑⦃#i⦄ → ∃∃K,V. ⇩[0, i] L ≡ K.ⓓV.
+lemma crr_inv_lref: ∀G,L,i. ⦃G, L⦄ ⊢ ➡ 𝐑⦃#i⦄ → ∃∃K,V. ⇩[i] L ≡ K.ⓓV.
 /2 width=4 by crr_inv_lref_aux/ qed-.
 
-fact crr_inv_gref_aux: ∀G,L,T,p. ⦃G, L⦄ ⊢ 𝐑⦃T⦄ → T = §p → ⊥.
+fact crr_inv_gref_aux: ∀G,L,T,p. ⦃G, L⦄ ⊢ ➡ 𝐑⦃T⦄ → T = §p → ⊥.
 #G #L #T #q * -L -T
 [ #L #K #V #i #HLK #H destruct
 | #L #V #T #_ #H destruct
@@ -91,10 +91,10 @@ fact crr_inv_gref_aux: ∀G,L,T,p. ⦃G, L⦄ ⊢ 𝐑⦃T⦄ → T = §p → 
 ]
 qed-.
 
-lemma crr_inv_gref: ∀G,L,p. ⦃G, L⦄ ⊢ 𝐑⦃§p⦄ → ⊥.
+lemma crr_inv_gref: ∀G,L,p. ⦃G, L⦄ ⊢ ➡ 𝐑⦃§p⦄ → ⊥.
 /2 width=6 by crr_inv_gref_aux/ qed-.
 
-lemma trr_inv_atom: ∀G,I. ⦃G, ⋆⦄ ⊢ 𝐑⦃⓪{I}⦄ → ⊥.
+lemma trr_inv_atom: ∀G,I. ⦃G, ⋆⦄ ⊢ ➡ 𝐑⦃⓪{I}⦄ → ⊥.
 #G * #i #H
 [ elim (crr_inv_sort … H)
 | elim (crr_inv_lref … H) -H #L #V #H
@@ -103,8 +103,8 @@ lemma trr_inv_atom: ∀G,I. ⦃G, ⋆⦄ ⊢ 𝐑⦃⓪{I}⦄ → ⊥.
 ]
 qed-.
 
-fact crr_inv_ib2_aux: ∀a,I,G,L,W,U,T. ib2 a I → ⦃G, L⦄ ⊢ 𝐑⦃T⦄ → T = ⓑ{a,I}W.U →
-                      ⦃G, L⦄ ⊢ 𝐑⦃W⦄ ∨ ⦃G, L.ⓑ{I}W⦄ ⊢ 𝐑⦃U⦄.
+fact crr_inv_ib2_aux: ∀a,I,G,L,W,U,T. ib2 a I → ⦃G, L⦄ ⊢ ➡ 𝐑⦃T⦄ → T = ⓑ{a,I}W.U →
+                      ⦃G, L⦄ ⊢ ➡ 𝐑⦃W⦄ ∨ ⦃G, L.ⓑ{I}W⦄ ⊢ ➡ 𝐑⦃U⦄.
 #G #b #J #L #W0 #U #T #HI * -L -T
 [ #L #K #V #i #_ #H destruct
 | #L #V #T #_ #H destruct
@@ -112,23 +112,23 @@ fact crr_inv_ib2_aux: ∀a,I,G,L,W,U,T. ib2 a I → ⦃G, L⦄ ⊢ 𝐑⦃T⦄ 
 | #I #L #V #T #H1 #H2 destruct
   elim H1 -H1 #H destruct
   elim HI -HI #H destruct
-| #a #I #L #V #T #_ #HV #H destruct /2 width=1/
-| #a #I #L #V #T #_ #HT #H destruct /2 width=1/
+| #a #I #L #V #T #_ #HV #H destruct /2 width=1 by or_introl/
+| #a #I #L #V #T #_ #HT #H destruct /2 width=1 by or_intror/
 | #a #L #V #W #T #H destruct
 | #a #L #V #W #T #H destruct
 ]
 qed-.
 
-lemma crr_inv_ib2: ∀a,I,G,L,W,T. ib2 a I → ⦃G, L⦄ ⊢ 𝐑⦃ⓑ{a,I}W.T⦄ →
-                   ⦃G, L⦄ ⊢ 𝐑⦃W⦄ ∨ ⦃G, L.ⓑ{I}W⦄ ⊢ 𝐑⦃T⦄.
+lemma crr_inv_ib2: ∀a,I,G,L,W,T. ib2 a I → ⦃G, L⦄ ⊢ ➡ 𝐑⦃ⓑ{a,I}W.T⦄ →
+                   ⦃G, L⦄ ⊢ ➡ 𝐑⦃W⦄ ∨ ⦃G, L.ⓑ{I}W⦄ ⊢ ➡ 𝐑⦃T⦄.
 /2 width=5 by crr_inv_ib2_aux/ qed-.
 
-fact crr_inv_appl_aux: ∀G,L,W,U,T. ⦃G, L⦄ ⊢ 𝐑⦃T⦄ → T = ⓐW.U →
-                       ∨∨ ⦃G, L⦄ ⊢ 𝐑⦃W⦄ | ⦃G, L⦄ ⊢ 𝐑⦃U⦄ | (𝐒⦃U⦄ → ⊥).
+fact crr_inv_appl_aux: ∀G,L,W,U,T. ⦃G, L⦄ ⊢ ➡ 𝐑⦃T⦄ → T = ⓐW.U →
+                       ∨∨ ⦃G, L⦄ ⊢ ➡ 𝐑⦃W⦄ | ⦃G, L⦄ ⊢ ➡ 𝐑⦃U⦄ | (𝐒⦃U⦄ → ⊥).
 #G #L #W0 #U #T * -L -T
 [ #L #K #V #i #_ #H destruct
-| #L #V #T #HV #H destruct /2 width=1/
-| #L #V #T #HT #H destruct /2 width=1/
+| #L #V #T #HV #H destruct /2 width=1 by or3_intro0/
+| #L #V #T #HT #H destruct /2 width=1 by or3_intro1/
 | #I #L #V #T #H1 #H2 destruct
   elim H1 -H1 #H destruct
 | #a #I #L #V #T #_ #_ #H destruct
@@ -140,6 +140,6 @@ fact crr_inv_appl_aux: ∀G,L,W,U,T. ⦃G, L⦄ ⊢ 𝐑⦃T⦄ → T = ⓐW.U 
 ]
 qed-.
 
-lemma crr_inv_appl: ∀G,L,V,T. ⦃G, L⦄ ⊢ 𝐑⦃ⓐV.T⦄ →
-                              ∨∨ ⦃G, L⦄ ⊢ 𝐑⦃V⦄ | ⦃G, L⦄ ⊢ 𝐑⦃T⦄ | (𝐒⦃T⦄ → ⊥).
+lemma crr_inv_appl: ∀G,L,V,T. ⦃G, L⦄ ⊢ ➡ 𝐑⦃ⓐV.T⦄ →
+                              ∨∨ ⦃G, L⦄ ⊢ ➡ 𝐑⦃V⦄ | ⦃G, L⦄ ⊢ ➡ 𝐑⦃T⦄ | (𝐒⦃T⦄ → ⊥).
 /2 width=3 by crr_inv_appl_aux/ qed-.