partial commit: just the components before "static" ...

[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 0aa31fe72cddb732b2265991f07283b32521523d..d9509e17a509d1a5156124fbb3d67d653d396445 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/cir.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/cir.ma
@@ -17,39 +17,39 @@ include "basic_2/reduction/crr.ma".
 
 (* CONTEXT-SENSITIVE IRREDUCIBLE TERMS **************************************)
 
-definition cir: lenv → predicate term ≝ λL,T. L ⊢ 𝐑⦃T⦄ → ⊥.
+definition cir: lenv → predicate term ≝ λL,T. ⦃G, L⦄ ⊢ 𝐑⦃T⦄ → ⊥.
 
 interpretation "context-sensitive irreducibility (term)"
    'NotReducible L T = (cir L T).
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma cir_inv_delta: ∀L,K,V,i. ⇩[0, i] L ≡ K.ⓓV → L ⊢ 𝐈⦃#i⦄ → ⊥.
+lemma cir_inv_delta: ∀L,K,V,i. ⇩[0, i] L ≡ K.ⓓV → ⦃G, L⦄ ⊢ 𝐈⦃#i⦄ → ⊥.
 /3 width=3/ qed-.
 
-lemma cir_inv_ri2: ∀I,L,V,T. ri2 I → L ⊢ 𝐈⦃②{I}V.T⦄ → ⊥.
+lemma cir_inv_ri2: ∀I,L,V,T. ri2 I → ⦃G, L⦄ ⊢ 𝐈⦃②{I}V.T⦄ → ⊥.
 /3 width=1/ qed-.
 
-lemma cir_inv_ib2: ∀a,I,L,V,T. ib2 a I → L ⊢ 𝐈⦃ⓑ{a,I}V.T⦄ →
-                   L ⊢ 𝐈⦃V⦄ ∧ L.ⓑ{I}V ⊢ 𝐈⦃T⦄.
+lemma cir_inv_ib2: ∀a,I,L,V,T. ib2 a I → ⦃G, L⦄ ⊢ 𝐈⦃ⓑ{a,I}V.T⦄ →
+                   ⦃G, L⦄ ⊢ 𝐈⦃V⦄ ∧ L.ⓑ{I}V ⊢ 𝐈⦃T⦄.
 /4 width=1/ qed-.
 
-lemma cir_inv_bind: ∀a,I,L,V,T. L ⊢ 𝐈⦃ⓑ{a,I}V.T⦄ →
-                    ∧∧ L ⊢ 𝐈⦃V⦄ & L.ⓑ{I}V ⊢ 𝐈⦃T⦄ & ib2 a I.
+lemma cir_inv_bind: ∀a,I,L,V,T. ⦃G, L⦄ ⊢ 𝐈⦃ⓑ{a,I}V.T⦄ →
+                    ∧∧ ⦃G, L⦄ ⊢ 𝐈⦃V⦄ & L.ⓑ{I}V ⊢ 𝐈⦃T⦄ & ib2 a I.
 #a * [ elim a -a ]
 [ #L #V #T #H elim H -H /3 width=1/
 |*: #L #V #T #H elim (cir_inv_ib2 … H) -H /2 width=1/ /3 width=1/
 ]
 qed-.
 
-lemma cir_inv_appl: ∀L,V,T. L ⊢ 𝐈⦃ⓐV.T⦄ → ∧∧ L ⊢ 𝐈⦃V⦄ & L ⊢ 𝐈⦃T⦄ & 𝐒⦃T⦄.
+lemma cir_inv_appl: ∀L,V,T. ⦃G, L⦄ ⊢ 𝐈⦃ⓐV.T⦄ → ∧∧ ⦃G, L⦄ ⊢ 𝐈⦃V⦄ & ⦃G, L⦄ ⊢ 𝐈⦃T⦄ & 𝐒⦃T⦄.
 #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/
 qed-.
 
-lemma cir_inv_flat: ∀I,L,V,T. L ⊢ 𝐈⦃ⓕ{I}V.T⦄ →
-                    ∧∧ L ⊢ 𝐈⦃V⦄ & L ⊢ 𝐈⦃T⦄ & 𝐒⦃T⦄ & I = Appl.
+lemma cir_inv_flat: ∀I,L,V,T. ⦃G, L⦄ ⊢ 𝐈⦃ⓕ{I}V.T⦄ →
+                    ∧∧ ⦃G, L⦄ ⊢ 𝐈⦃V⦄ & ⦃G, L⦄ ⊢ 𝐈⦃T⦄ & 𝐒⦃T⦄ & I = Appl.
 * #L #V #T #H
 [ elim (cir_inv_appl … H) -H /2 width=1/
 | elim (cir_inv_ri2 … H) -H /2 width=1/
@@ -58,21 +58,21 @@ qed-.
 
 (* Basic properties *********************************************************)
 
-lemma cir_sort: ∀L,k. L ⊢ 𝐈⦃⋆k⦄.
+lemma cir_sort: ∀L,k. ⦃G, L⦄ ⊢ 𝐈⦃⋆k⦄.
 /2 width=3 by crr_inv_sort/ qed.
 
-lemma cir_gref: ∀L,p. L ⊢ 𝐈⦃§p⦄.
+lemma cir_gref: ∀L,p. ⦃G, L⦄ ⊢ 𝐈⦃§p⦄.
 /2 width=3 by crr_inv_gref/ qed.
 
 lemma tir_atom: ∀I. ⋆ ⊢ 𝐈⦃⓪{I}⦄.
 /2 width=2 by trr_inv_atom/ qed.
 
-lemma cir_ib2: ∀a,I,L,V,T. ib2 a I → L ⊢ 𝐈⦃V⦄ → L.ⓑ{I}V ⊢ 𝐈⦃T⦄ → L ⊢ 𝐈⦃ⓑ{a,I}V.T⦄.
+lemma cir_ib2: ∀a,I,L,V,T. ib2 a I → ⦃G, L⦄ ⊢ 𝐈⦃V⦄ → L.ⓑ{I}V ⊢ 𝐈⦃T⦄ → ⦃G, L⦄ ⊢ 𝐈⦃ⓑ{a,I}V.T⦄.
 #a #I #L #V #T #HI #HV #HT #H
 elim (crr_inv_ib2 … HI H) -HI -H /2 width=1/
 qed.
 
-lemma cir_appl: ∀L,V,T. L ⊢ 𝐈⦃V⦄ → L ⊢ 𝐈⦃T⦄ →  𝐒⦃T⦄ → L ⊢ 𝐈⦃ⓐV.T⦄.
+lemma cir_appl: ∀L,V,T. ⦃G, L⦄ ⊢ 𝐈⦃V⦄ → ⦃G, L⦄ ⊢ 𝐈⦃T⦄ →  𝐒⦃T⦄ → ⦃G, L⦄ ⊢ 𝐈⦃ⓐV.T⦄.
 #L #V #T #HV #HT #H1 #H2
 elim (crr_inv_appl … H2) -H2 /2 width=1/
 qed.