- new component "s_transition" for the restored fqu and fquq

[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 a8a5bcc9cae21a06b95d99b151192fd1398fb83b..412297546be35b30893396504a2dcc35a00dc568 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/cir.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/cir.ma
@@ -12,19 +12,19 @@
 (*                                                                        *)
 (**************************************************************************)
 
-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⦄ → ⊥.
 
-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 ≡ K.ⓓV → ⦃G, L⦄ ⊢ ➡ 𝐈⦃#i⦄ → ⊥.
+lemma cir_inv_delta: â\88\80G,L,K,V,i. â¬\87[i] L ≡ K.ⓓV → ⦃G, L⦄ ⊢ ➡ 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⦄ → ⊥.
@@ -43,7 +43,7 @@ qed-.
 
 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/
+#G #L #V #T #HVT @and3_intro /3 width=1 by crr_appl_sn, crr_appl_dx/
 generalize in match HVT; -HVT elim T -T //
 * // #a * #U #T #_ #_ #H elim H -H /2 width=1 by crr_beta, crr_theta/
 qed-.
@@ -58,7 +58,7 @@ qed-.
 
 (* Basic properties *********************************************************)
 
-lemma cir_sort: ∀G,L,k. ⦃G, L⦄ ⊢ ➡ 𝐈⦃⋆k⦄.
+lemma cir_sort: ∀G,L,s. ⦃G, L⦄ ⊢ ➡ 𝐈⦃⋆s⦄.
 /2 width=4 by crr_inv_sort/ qed.
 
 lemma cir_gref: ∀G,L,p. ⦃G, L⦄ ⊢ ➡ 𝐈⦃§p⦄.