notational change of lift, drop, and gget

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / reduction / cir.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/cir.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/cir.ma
index 35a28700a457df918cbf976fd339b724f9075bbb..576633954bd138547b93255e7853daeb456eb579 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/cir.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/cir.ma
@@ -12,44 +12,44 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/notreducible_3.ma".
+include "basic_2/notation/relations/prednotreducible_3.ma".
 include "basic_2/reduction/crr.ma".
 
-(* CONTEXT-SENSITIVE IRREDUCIBLE TERMS **************************************)
+(* IRREDUCIBLE TERMS FOR CONTEXT-SENSITIVE REDUCTION ************************)
 
-definition cir: relation3 genv lenv term ≝ λG,L,T. ⦃G, L⦄ ⊢ 𝐑⦃T⦄ → ⊥.
+definition cir: relation3 genv lenv term ≝ λG,L,T. ⦃G, L⦄ ⊢ ➡ 𝐑⦃T⦄ → ⊥.
 
-interpretation "context-sensitive irreducibility (term)"
-   'NotReducible G L T = (cir G L T).
+interpretation "irreducibility for context-sensitive reduction (term)"
+   'PRedNotReducible G L T = (cir G L T).
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma cir_inv_delta: â\88\80G,L,K,V,i. â\87©[i] L â\89¡ K.â\93\93V â\86\92 â¦\83G, Lâ¦\84 â\8a¢ 𝐈⦃#i⦄ → ⊥.
+lemma cir_inv_delta: â\88\80G,L,K,V,i. â¬\87[i] L â\89¡ K.â\93\93V â\86\92 â¦\83G, Lâ¦\84 â\8a¢ â\9e¡ 𝐈⦃#i⦄ → ⊥.
 /3 width=3 by crr_delta/ qed-.
 
-lemma cir_inv_ri2: ∀I,G,L,V,T. ri2 I → ⦃G, L⦄ ⊢ 𝐈⦃②{I}V.T⦄ → ⊥.
+lemma cir_inv_ri2: ∀I,G,L,V,T. ri2 I → ⦃G, L⦄ ⊢ ➡ 𝐈⦃②{I}V.T⦄ → ⊥.
 /3 width=1 by crr_ri2/ qed-.
 
-lemma cir_inv_ib2: ∀a,I,G,L,V,T. ib2 a I → ⦃G, L⦄ ⊢ 𝐈⦃ⓑ{a,I}V.T⦄ →
-                   ⦃G, L⦄ ⊢ 𝐈⦃V⦄ ∧ ⦃G, L.ⓑ{I}V⦄ ⊢ 𝐈⦃T⦄.
+lemma cir_inv_ib2: ∀a,I,G,L,V,T. ib2 a I → ⦃G, L⦄ ⊢ ➡ 𝐈⦃ⓑ{a,I}V.T⦄ →
+                   ⦃G, L⦄ ⊢ ➡ 𝐈⦃V⦄ ∧ ⦃G, L.ⓑ{I}V⦄ ⊢ ➡ 𝐈⦃T⦄.
 /4 width=1 by crr_ib2_sn, crr_ib2_dx, conj/ qed-.
 
-lemma cir_inv_bind: ∀a,I,G,L,V,T. ⦃G, L⦄ ⊢ 𝐈⦃ⓑ{a,I}V.T⦄ →
-                    ∧∧ ⦃G, L⦄ ⊢ 𝐈⦃V⦄ & ⦃G, L.ⓑ{I}V⦄ ⊢ 𝐈⦃T⦄ & ib2 a I.
+lemma cir_inv_bind: ∀a,I,G,L,V,T. ⦃G, L⦄ ⊢ ➡ 𝐈⦃ⓑ{a,I}V.T⦄ →
+                    ∧∧ ⦃G, L⦄ ⊢ ➡ 𝐈⦃V⦄ & ⦃G, L.ⓑ{I}V⦄ ⊢ ➡ 𝐈⦃T⦄ & ib2 a I.
 #a * [ elim a -a ]
 #G #L #V #T #H [ elim H -H /3 width=1 by crr_ri2, or_introl/ ]
 elim (cir_inv_ib2 … H) -H /3 width=1 by and3_intro, or_introl/
 qed-.
 
-lemma cir_inv_appl: ∀G,L,V,T. ⦃G, L⦄ ⊢ 𝐈⦃ⓐV.T⦄ →
-                    ∧∧ ⦃G, L⦄ ⊢ 𝐈⦃V⦄ & ⦃G, L⦄ ⊢ 𝐈⦃T⦄ & 𝐒⦃T⦄.
+lemma cir_inv_appl: ∀G,L,V,T. ⦃G, L⦄ ⊢ ➡ 𝐈⦃ⓐV.T⦄ →
+                    ∧∧ ⦃G, L⦄ ⊢ ➡ 𝐈⦃V⦄ & ⦃G, L⦄ ⊢ ➡ 𝐈⦃T⦄ & 𝐒⦃T⦄.
 #G #L #V #T #HVT @and3_intro /3 width=1/
 generalize in match HVT; -HVT elim T -T //
 * // #a * #U #T #_ #_ #H elim H -H /2 width=1 by crr_beta, crr_theta/
 qed-.
 
-lemma cir_inv_flat: ∀I,G,L,V,T. ⦃G, L⦄ ⊢ 𝐈⦃ⓕ{I}V.T⦄ →
-                    ∧∧ ⦃G, L⦄ ⊢ 𝐈⦃V⦄ & ⦃G, L⦄ ⊢ 𝐈⦃T⦄ & 𝐒⦃T⦄ & I = Appl.
+lemma cir_inv_flat: ∀I,G,L,V,T. ⦃G, L⦄ ⊢ ➡ 𝐈⦃ⓕ{I}V.T⦄ →
+                    ∧∧ ⦃G, L⦄ ⊢ ➡ 𝐈⦃V⦄ & ⦃G, L⦄ ⊢ ➡ 𝐈⦃T⦄ & 𝐒⦃T⦄ & I = Appl.
 * #G #L #V #T #H
 [ elim (cir_inv_appl … H) -H /2 width=1 by and4_intro/
 | elim (cir_inv_ri2 … H) -H //
@@ -58,22 +58,22 @@ qed-.
 
 (* Basic properties *********************************************************)
 
-lemma cir_sort: ∀G,L,k. ⦃G, L⦄ ⊢ 𝐈⦃⋆k⦄.
+lemma cir_sort: ∀G,L,k. ⦃G, L⦄ ⊢ ➡ 𝐈⦃⋆k⦄.
 /2 width=4 by crr_inv_sort/ qed.
 
-lemma cir_gref: ∀G,L,p. ⦃G, L⦄ ⊢ 𝐈⦃§p⦄.
+lemma cir_gref: ∀G,L,p. ⦃G, L⦄ ⊢ ➡ 𝐈⦃§p⦄.
 /2 width=4 by crr_inv_gref/ qed.
 
-lemma tir_atom: ∀G,I. ⦃G, ⋆⦄ ⊢ 𝐈⦃⓪{I}⦄.
+lemma tir_atom: ∀G,I. ⦃G, ⋆⦄ ⊢ ➡ 𝐈⦃⓪{I}⦄.
 /2 width=3 by trr_inv_atom/ qed.
 
 lemma cir_ib2: ∀a,I,G,L,V,T.
-               ib2 a I → ⦃G, L⦄ ⊢ 𝐈⦃V⦄ → ⦃G, L.ⓑ{I}V⦄ ⊢ 𝐈⦃T⦄ → ⦃G, L⦄ ⊢ 𝐈⦃ⓑ{a,I}V.T⦄.
+               ib2 a I → ⦃G, L⦄ ⊢ ➡ 𝐈⦃V⦄ → ⦃G, L.ⓑ{I}V⦄ ⊢ ➡ 𝐈⦃T⦄ → ⦃G, L⦄ ⊢ ➡ 𝐈⦃ⓑ{a,I}V.T⦄.
 #a #I #G #L #V #T #HI #HV #HT #H
 elim (crr_inv_ib2 … HI H) -HI -H /2 width=1 by/
 qed.
 
-lemma cir_appl: ∀G,L,V,T. ⦃G, L⦄ ⊢ 𝐈⦃V⦄ → ⦃G, L⦄ ⊢ 𝐈⦃T⦄ →  𝐒⦃T⦄ → ⦃G, L⦄ ⊢ 𝐈⦃ⓐV.T⦄.
+lemma cir_appl: ∀G,L,V,T. ⦃G, L⦄ ⊢ ➡ 𝐈⦃V⦄ → ⦃G, L⦄ ⊢ ➡ 𝐈⦃T⦄ →  𝐒⦃T⦄ → ⦃G, L⦄ ⊢ ➡ 𝐈⦃ⓐV.T⦄.
 #G #L #V #T #HV #HT #H1 #H2
 elim (crr_inv_appl … H2) -H2 /2 width=1 by/
 qed.