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

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / csn_alt.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/csn_alt.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/csn_alt.ma
index 954cb9c014ef7bd600e9bf444b072c3f39f436fb..07716de628947c6ff614d546a2d1e54a5bcea902 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/csn_alt.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/csn_alt.ma
@@ -29,10 +29,10 @@ interpretation
 (* Basic eliminators ********************************************************)
 
 lemma csna_ind: ∀h,g,L. ∀R:predicate term.
-                (∀T1. ⦃h, L⦄ ⊢ ⬊⬊*[g] T1 →
-                      (∀T2. ⦃h, L⦄ ⊢ T1 ➡*[g] T2 → (T1 = T2 → ⊥) → R T2) → R T1
+                (∀T1. ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T1 →
+                      (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → (T1 = T2 → ⊥) → R T2) → R T1
                 ) →
-                ∀T. ⦃h, L⦄ ⊢ ⬊⬊*[g] T → R T.
+                ∀T. ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T → R T.
 #h #g #L #R #H0 #T1 #H elim H -T1 #T1 #HT1 #IHT1
 @H0 -H0 /3 width=1/ -IHT1 /4 width=1/
 qed-.
@@ -41,18 +41,18 @@ qed-.
 
 (* Basic_1: was just: sn3_intro *)
 lemma csna_intro: ∀h,g,L,T1.
-                  (∀T2. ⦃h, L⦄ ⊢ T1 ➡*[g] T2 → (T1 = T2 → ⊥) → ⦃h, L⦄ ⊢ ⬊⬊*[g] T2) →
-                  ⦃h, L⦄ ⊢ ⬊⬊*[g] T1.
+                  (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → (T1 = T2 → ⊥) → ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T2) →
+                  ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T1.
 /4 width=1/ qed.
 
 fact csna_intro_aux: ∀h,g,L,T1. (
-                        ∀T,T2. ⦃h, L⦄ ⊢ T ➡*[g] T2 → T1 = T → (T1 = T2 → ⊥) → ⦃h, L⦄ ⊢ ⬊⬊*[g] T2
-                     ) → ⦃h, L⦄ ⊢ ⬊⬊*[g] T1.
+                        ∀T,T2. ⦃G, L⦄ ⊢ T ➡*[h, g] T2 → T1 = T → (T1 = T2 → ⊥) → ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T2
+                     ) → ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T1.
 /4 width=3/ qed-.
 
 (* Basic_1: was just: sn3_pr3_trans (old version) *)
-lemma csna_cpxs_trans: ∀h,g,L,T1. ⦃h, L⦄ ⊢ ⬊⬊*[g] T1 →
-                       ∀T2. ⦃h, L⦄ ⊢ T1 ➡*[g] T2 → ⦃h, L⦄ ⊢ ⬊⬊*[g] T2.
+lemma csna_cpxs_trans: ∀h,g,L,T1. ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T1 →
+                       ∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T2.
 #h #g #L #T1 #H elim H -T1 #T1 #HT1 #IHT1 #T2 #HLT12
 @csna_intro #T #HLT2 #HT2
 elim (term_eq_dec T1 T2) #HT12
@@ -62,8 +62,8 @@ qed.
 
 (* Basic_1: was just: sn3_pr2_intro (old version) *)
 lemma csna_intro_cpx: ∀h,g,L,T1. (
-                         ∀T2. ⦃h, L⦄ ⊢ T1 ➡[g] T2 → (T1 = T2 → ⊥) → ⦃h, L⦄ ⊢ ⬊⬊*[g] T2
-                      ) → ⦃h, L⦄ ⊢ ⬊⬊*[g] T1.
+                         ∀T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 → (T1 = T2 → ⊥) → ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T2
+                      ) → ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T1.
 #h #g #L #T1 #H
 @csna_intro_aux #T #T2 #H @(cpxs_ind_dx … H) -T
 [ -H #H destruct #H
@@ -78,27 +78,27 @@ qed.
 
 (* Main properties **********************************************************)
 
-theorem csn_csna: ∀h,g,L,T. ⦃h, L⦄ ⊢ ⬊*[g] T → ⦃h, L⦄ ⊢ ⬊⬊*[g] T.
+theorem csn_csna: ∀h,g,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T.
 #h #g #L #T #H @(csn_ind … H) -T /4 width=1/
 qed.
 
-theorem csna_csn: ∀h,g,L,T. ⦃h, L⦄ ⊢ ⬊⬊*[g] T → ⦃h, L⦄ ⊢ ⬊*[g] T.
+theorem csna_csn: ∀h,g,L,T. ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T → ⦃G, L⦄ ⊢ ⬊*[h, g] T.
 #h #g #L #T #H @(csna_ind … H) -T /4 width=1/
 qed.
 
 (* Basic_1: was just: sn3_pr3_trans *)
-lemma csn_cpxs_trans: ∀h,g,L,T1. ⦃h, L⦄ ⊢ ⬊*[g] T1 →
-                      ∀T2. ⦃h, L⦄ ⊢ T1 ➡*[g] T2 → ⦃h, L⦄ ⊢ ⬊*[g] T2.
+lemma csn_cpxs_trans: ∀h,g,L,T1. ⦃G, L⦄ ⊢ ⬊*[h, g] T1 →
+                      ∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → ⦃G, L⦄ ⊢ ⬊*[h, g] T2.
 #h #g #L #T1 #HT1 #T2 #H @(cpxs_ind … H) -T2 // /2 width=3 by csn_cpx_trans/
 qed-.
 
 (* Main eliminators *********************************************************)
 
 lemma csn_ind_alt: ∀h,g,L. ∀R:predicate term.
-                   (∀T1. ⦃h, L⦄ ⊢ ⬊*[g] T1 →
-                         (∀T2. ⦃h, L⦄ ⊢ T1 ➡*[g] T2 → (T1 = T2 → ⊥) → R T2) → R T1
+                   (∀T1. ⦃G, L⦄ ⊢ ⬊*[h, g] T1 →
+                         (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → (T1 = T2 → ⊥) → R T2) → R T1
                    ) →
-                   ∀T. ⦃h, L⦄ ⊢ ⬊*[g] T → R T.
+                   ∀T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → R T.
 #h #g #L #R #H0 #T1 #H @(csna_ind … (csn_csna … H)) -T1 #T1 #HT1 #IHT1
 @H0 -H0 /2 width=1/ -HT1 /3 width=1/
 qed-.