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

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/cnx.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/cnx.ma
index 8e6dd66ba0d6694f8516150737486fbd9e96fbcd..5c97081f59a4e4e775a4c31547ba1673a15137fc 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/cnx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/cnx.ma
@@ -27,37 +27,37 @@ interpretation
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma cnx_inv_sort: ∀h,g,L,k. ⦃h, L⦄ ⊢ 𝐍[g]⦃⋆k⦄ → deg h g k 0.
+lemma cnx_inv_sort: ∀h,g,L,k. ⦃G, L⦄ ⊢ 𝐍[h, g]⦃⋆k⦄ → deg h g k 0.
 #h #g #L #k #H elim (deg_total h g k)
 #l @(nat_ind_plus … l) -l // #l #_ #Hkl
 lapply (H (⋆(next h k)) ?) -H /2 width=2/ -L -l #H destruct -H -e0 (**) (* destruct does not remove some premises *)
 lapply (next_lt h k) >e1 -e1 #H elim (lt_refl_false … H)
 qed-.
 
-lemma cnx_inv_delta: ∀h,g,I,L,K,V,i. ⇩[0, i] L ≡ K.ⓑ{I}V → ⦃h, L⦄ ⊢ 𝐍[g]⦃#i⦄ → ⊥.
+lemma cnx_inv_delta: ∀h,g,I,L,K,V,i. ⇩[0, i] L ≡ K.ⓑ{I}V → ⦃G, L⦄ ⊢ 𝐍[h, g]⦃#i⦄ → ⊥.
 #h #g #I #L #K #V #i #HLK #H
 elim (lift_total V 0 (i+1)) #W #HVW
 lapply (H W ?) -H [ /3 width=7/ ] -HLK #H destruct
 elim (lift_inv_lref2_be … HVW) -HVW //
 qed-.
 
-lemma cnx_inv_abst: ∀h,g,a,L,V,T. ⦃h, L⦄ ⊢ 𝐍[g]⦃ⓛ{a}V.T⦄ →
-                    ⦃h, L⦄ ⊢ 𝐍[g]⦃V⦄ ∧ ⦃h, L.ⓛV⦄ ⊢ 𝐍[g]⦃T⦄.
+lemma cnx_inv_abst: ∀h,g,a,L,V,T. ⦃G, L⦄ ⊢ 𝐍[h, g]⦃ⓛ{a}V.T⦄ →
+                    ⦃G, L⦄ ⊢ 𝐍[h, g]⦃V⦄ ∧ ⦃h, L.ⓛV⦄ ⊢ 𝐍[h, g]⦃T⦄.
 #h #g #a #L #V1 #T1 #HVT1 @conj
 [ #V2 #HV2 lapply (HVT1 (ⓛ{a}V2.T1) ?) -HVT1 /2 width=2/ -HV2 #H destruct //
 | #T2 #HT2 lapply (HVT1 (ⓛ{a}V1.T2) ?) -HVT1 /2 width=2/ -HT2 #H destruct //
 ]
 qed-.
 
-lemma cnx_inv_abbr: ∀h,g,L,V,T. ⦃h, L⦄ ⊢ 𝐍[g]⦃-ⓓV.T⦄ →
-                    ⦃h, L⦄ ⊢ 𝐍[g]⦃V⦄ ∧ ⦃h, L.ⓓV⦄ ⊢ 𝐍[g]⦃T⦄.
+lemma cnx_inv_abbr: ∀h,g,L,V,T. ⦃G, L⦄ ⊢ 𝐍[h, g]⦃-ⓓV.T⦄ →
+                    ⦃G, L⦄ ⊢ 𝐍[h, g]⦃V⦄ ∧ ⦃h, L.ⓓV⦄ ⊢ 𝐍[h, g]⦃T⦄.
 #h #g #L #V1 #T1 #HVT1 @conj
 [ #V2 #HV2 lapply (HVT1 (-ⓓV2.T1) ?) -HVT1 /2 width=2/ -HV2 #H destruct //
 | #T2 #HT2 lapply (HVT1 (-ⓓV1.T2) ?) -HVT1 /2 width=2/ -HT2 #H destruct //
 ]
 qed-.
 
-lemma cnx_inv_zeta: ∀h,g,L,V,T. ⦃h, L⦄ ⊢ 𝐍[g]⦃+ⓓV.T⦄ → ⊥.
+lemma cnx_inv_zeta: ∀h,g,L,V,T. ⦃G, L⦄ ⊢ 𝐍[h, g]⦃+ⓓV.T⦄ → ⊥.
 #h #g #L #V #T #H elim (is_lift_dec T 0 1)
 [ * #U #HTU
   lapply (H U ?) -H /2 width=3/ #H destruct
@@ -68,8 +68,8 @@ lemma cnx_inv_zeta: ∀h,g,L,V,T. ⦃h, L⦄ ⊢ 𝐍[g]⦃+ⓓV.T⦄ → ⊥.
 ]
 qed-.
 
-lemma cnx_inv_appl: ∀h,g,L,V,T. ⦃h, L⦄ ⊢ 𝐍[g]⦃ⓐV.T⦄ →
-                    ∧∧ ⦃h, L⦄ ⊢ 𝐍[g]⦃V⦄ & ⦃h, L⦄ ⊢ 𝐍[g]⦃T⦄ & 𝐒⦃T⦄.
+lemma cnx_inv_appl: ∀h,g,L,V,T. ⦃G, L⦄ ⊢ 𝐍[h, g]⦃ⓐV.T⦄ →
+                    ∧∧ ⦃G, L⦄ ⊢ 𝐍[h, g]⦃V⦄ & ⦃G, L⦄ ⊢ 𝐍[h, g]⦃T⦄ & 𝐒⦃T⦄.
 #h #g #L #V1 #T1 #HVT1 @and3_intro
 [ #V2 #HV2 lapply (HVT1 (ⓐV2.T1) ?) -HVT1 /2 width=1/ -HV2 #H destruct //
 | #T2 #HT2 lapply (HVT1 (ⓐV1.T2) ?) -HVT1 /2 width=1/ -HT2 #H destruct //
@@ -80,43 +80,43 @@ lemma cnx_inv_appl: ∀h,g,L,V,T. ⦃h, L⦄ ⊢ 𝐍[g]⦃ⓐV.T⦄ →
 ]
 qed-.
 
-lemma cnx_inv_tau: ∀h,g,L,V,T. ⦃h, L⦄ ⊢ 𝐍[g]⦃ⓝV.T⦄ → ⊥.
+lemma cnx_inv_tau: ∀h,g,L,V,T. ⦃G, L⦄ ⊢ 𝐍[h, g]⦃ⓝV.T⦄ → ⊥.
 #h #g #L #V #T #H lapply (H T ?) -H /2 width=1/ #H
 @discr_tpair_xy_y //
 qed-.
 
 (* Basic forward lemmas *****************************************************)
 
-lemma cnx_fwd_cnr: ∀h,g,L,T. ⦃h, L⦄ ⊢ 𝐍[g]⦃T⦄ → L ⊢ 𝐍⦃T⦄.
+lemma cnx_fwd_cnr: ∀h,g,L,T. ⦃G, L⦄ ⊢ 𝐍[h, g]⦃T⦄ → ⦃G, L⦄ ⊢ 𝐍⦃T⦄.
 #h #g #L #T #H #U #HTU
 @H /2 width=1/ (**) (* auto fails because a δ-expansion gets in the way *)
 qed-.
 
 (* Basic properties *********************************************************)
 
-lemma cnx_sort: ∀h,g,L,k. deg h g k 0 → ⦃h, L⦄ ⊢ 𝐍[g]⦃⋆k⦄.
+lemma cnx_sort: ∀h,g,L,k. deg h g k 0 → ⦃G, L⦄ ⊢ 𝐍[h, g]⦃⋆k⦄.
 #h #g #L #k #Hk #X #H elim (cpx_inv_sort1 … H) -H // * #l #Hkl #_
 lapply (deg_mono … Hkl Hk) -h -L <plus_n_Sm #H destruct 
 qed.
 
-lemma cnx_sort_iter: ∀h,g,L,k,l. deg h g k l → ⦃h, L⦄ ⊢ 𝐍[g]⦃⋆((next h)^l k)⦄.
+lemma cnx_sort_iter: ∀h,g,L,k,l. deg h g k l → ⦃G, L⦄ ⊢ 𝐍[h, g]⦃⋆((next h)^l k)⦄.
 #h #g #L #k #l #Hkl
 lapply (deg_iter … l Hkl) -Hkl <minus_n_n /2 width=1/
 qed.
 
-lemma cnx_abst: ∀h,g,a,L,W,T. ⦃h, L⦄ ⊢ 𝐍[g]⦃W⦄ → ⦃h, L.ⓛW⦄ ⊢ 𝐍[g]⦃T⦄ →
-                ⦃h, L⦄ ⊢ 𝐍[g]⦃ⓛ{a}W.T⦄.
+lemma cnx_abst: ∀h,g,a,L,W,T. ⦃G, L⦄ ⊢ 𝐍[h, g]⦃W⦄ → ⦃h, L.ⓛW⦄ ⊢ 𝐍[h, g]⦃T⦄ →
+                ⦃G, L⦄ ⊢ 𝐍[h, g]⦃ⓛ{a}W.T⦄.
 #h #g #a #L #W #T #HW #HT #X #H
 elim (cpx_inv_abst1 … H) -H #W0 #T0 #HW0 #HT0 #H destruct
 >(HW … HW0) -W0 >(HT … HT0) -T0 //
 qed.
 
-lemma cnx_appl_simple: ∀h,g,L,V,T. ⦃h, L⦄ ⊢ 𝐍[g]⦃V⦄ → ⦃h, L⦄ ⊢ 𝐍[g]⦃T⦄ → 𝐒⦃T⦄ →
-                       ⦃h, L⦄ ⊢ 𝐍[g]⦃ⓐV.T⦄.
+lemma cnx_appl_simple: ∀h,g,L,V,T. ⦃G, L⦄ ⊢ 𝐍[h, g]⦃V⦄ → ⦃G, L⦄ ⊢ 𝐍[h, g]⦃T⦄ → 𝐒⦃T⦄ →
+                       ⦃G, L⦄ ⊢ 𝐍[h, g]⦃ⓐV.T⦄.
 #h #g #L #V #T #HV #HT #HS #X #H
 elim (cpx_inv_appl1_simple … H) -H // #V0 #T0 #HV0 #HT0 #H destruct
 >(HV … HV0) -V0 >(HT … HT0) -T0 //
 qed.
 
-axiom cnx_dec: ∀h,g,L,T1. ⦃h, L⦄ ⊢ 𝐍[g]⦃T1⦄ ∨
-               ∃∃T2. ⦃h, L⦄ ⊢ T1 ➡[g] T2 & (T1 = T2 → ⊥).
+axiom cnx_dec: ∀h,g,L,T1. ⦃G, L⦄ ⊢ 𝐍[h, g]⦃T1⦄ ∨
+               ∃∃T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 & (T1 = T2 → ⊥).