- commit of the "s_computation" component ...

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/csx_alt.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/csx_alt.ma
index a6f46c787c3f8b782053636d3d956e197c8d9627..0b9b29799f5463b0a20b6750ecaf6856bbe3c5db 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/csx_alt.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/csx_alt.ma
@@ -20,44 +20,44 @@ include "basic_2/computation/csx.ma".
 
 (* alternative definition of csx *)
 definition csxa: ∀h. sd h → relation3 genv lenv term ≝
-                 λh,g,G,L. SN … (cpxs h g G L) (eq …).
+                 λh,o,G,L. SN … (cpxs h o G L) (eq …).
 
 interpretation
    "context-sensitive extended strong normalization (term) alternative"
-   'SNAlt h g G L T = (csxa h g G L T).
+   'SNAlt h o G L T = (csxa h o G L T).
 
 (* Basic eliminators ********************************************************)
 
-lemma csxa_ind: ∀h,g,G,L. ∀R:predicate term.
-                (∀T1. ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T1 →
-                      (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → (T1 = T2 → ⊥) → R T2) → R T1
+lemma csxa_ind: ∀h,o,G,L. ∀R:predicate term.
+                (∀T1. ⦃G, L⦄ ⊢ ⬊⬊*[h, o] T1 →
+                      (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, o] T2 → (T1 = T2 → ⊥) → R T2) → R T1
                 ) →
-                ∀T. ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T → R T.
-#h #g #G #L #R #H0 #T1 #H elim H -T1 /5 width=1 by SN_intro/
+                ∀T. ⦃G, L⦄ ⊢ ⬊⬊*[h, o] T → R T.
+#h #o #G #L #R #H0 #T1 #H elim H -T1 /5 width=1 by SN_intro/
 qed-.
 
 (* Basic properties *********************************************************)
 
-lemma csx_intro_cpxs: ∀h,g,G,L,T1.
-                         (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → (T1 = T2 → ⊥) → ⦃G, L⦄ ⊢ ⬊*[h, g] T2) →
-                      ⦃G, L⦄ ⊢ ⬊*[h, g] T1.
+lemma csx_intro_cpxs: ∀h,o,G,L,T1.
+                         (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, o] T2 → (T1 = T2 → ⊥) → ⦃G, L⦄ ⊢ ⬊*[h, o] T2) →
+                      ⦃G, L⦄ ⊢ ⬊*[h, o] T1.
 /4 width=1 by cpx_cpxs, csx_intro/ qed.
 
 (* Basic_1: was just: sn3_intro *)
-lemma csxa_intro: ∀h,g,G,L,T1.
-                  (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → (T1 = T2 → ⊥) → ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T2) →
-                  ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T1.
+lemma csxa_intro: ∀h,o,G,L,T1.
+                  (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, o] T2 → (T1 = T2 → ⊥) → ⦃G, L⦄ ⊢ ⬊⬊*[h, o] T2) →
+                  ⦃G, L⦄ ⊢ ⬊⬊*[h, o] T1.
 /4 width=1 by SN_intro/ qed.
 
-fact csxa_intro_aux: ∀h,g,G,L,T1. (
-                        ∀T,T2. ⦃G, L⦄ ⊢ T ➡*[h, g] T2 → T1 = T → (T1 = T2 → ⊥) → ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T2
-                     ) → ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T1.
+fact csxa_intro_aux: ∀h,o,G,L,T1. (
+                        ∀T,T2. ⦃G, L⦄ ⊢ T ➡*[h, o] T2 → T1 = T → (T1 = T2 → ⊥) → ⦃G, L⦄ ⊢ ⬊⬊*[h, o] T2
+                     ) → ⦃G, L⦄ ⊢ ⬊⬊*[h, o] T1.
 /4 width=3 by csxa_intro/ qed-.
 
 (* Basic_1: was just: sn3_pr3_trans (old version) *)
-lemma csxa_cpxs_trans: ∀h,g,G,L,T1. ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T1 →
-                       ∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T2.
-#h #g #G #L #T1 #H elim H -T1 #T1 #HT1 #IHT1 #T2 #HLT12
+lemma csxa_cpxs_trans: ∀h,o,G,L,T1. ⦃G, L⦄ ⊢ ⬊⬊*[h, o] T1 →
+                       ∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, o] T2 → ⦃G, L⦄ ⊢ ⬊⬊*[h, o] T2.
+#h #o #G #L #T1 #H elim H -T1 #T1 #HT1 #IHT1 #T2 #HLT12
 @csxa_intro #T #HLT2 #HT2
 elim (eq_term_dec T1 T2) #HT12
 [ -IHT1 -HLT12 destruct /3 width=1 by/
@@ -65,10 +65,10 @@ elim (eq_term_dec T1 T2) #HT12
 qed.
 
 (* Basic_1: was just: sn3_pr2_intro (old version) *)
-lemma csxa_intro_cpx: ∀h,g,G,L,T1. (
-                         ∀T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 → (T1 = T2 → ⊥) → ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T2
-                      ) → ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T1.
-#h #g #G #L #T1 #H
+lemma csxa_intro_cpx: ∀h,o,G,L,T1. (
+                         ∀T2. ⦃G, L⦄ ⊢ T1 ➡[h, o] T2 → (T1 = T2 → ⊥) → ⦃G, L⦄ ⊢ ⬊⬊*[h, o] T2
+                      ) → ⦃G, L⦄ ⊢ ⬊⬊*[h, o] T1.
+#h #o #G #L #T1 #H
 @csxa_intro_aux #T #T2 #H @(cpxs_ind_dx … H) -T
 [ -H #H destruct #H
   elim H //
@@ -82,26 +82,26 @@ qed.
 
 (* Main properties **********************************************************)
 
-theorem csx_csxa: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T.
-#h #g #G #L #T #H @(csx_ind … H) -T /4 width=1 by csxa_intro_cpx/
+theorem csx_csxa: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, o] T → ⦃G, L⦄ ⊢ ⬊⬊*[h, o] T.
+#h #o #G #L #T #H @(csx_ind … H) -T /4 width=1 by csxa_intro_cpx/
 qed.
 
-theorem csxa_csx: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T → ⦃G, L⦄ ⊢ ⬊*[h, g] T.
-#h #g #G #L #T #H @(csxa_ind … H) -T /4 width=1 by cpx_cpxs, csx_intro/
+theorem csxa_csx: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ ⬊⬊*[h, o] T → ⦃G, L⦄ ⊢ ⬊*[h, o] T.
+#h #o #G #L #T #H @(csxa_ind … H) -T /4 width=1 by cpx_cpxs, csx_intro/
 qed.
 
 (* Basic_1: was just: sn3_pr3_trans *)
-lemma csx_cpxs_trans: ∀h,g,G,L,T1. ⦃G, L⦄ ⊢ ⬊*[h, g] T1 →
-                      ∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → ⦃G, L⦄ ⊢ ⬊*[h, g] T2.
-#h #g #G #L #T1 #HT1 #T2 #H @(cpxs_ind … H) -T2 /2 width=3 by csx_cpx_trans/
+lemma csx_cpxs_trans: ∀h,o,G,L,T1. ⦃G, L⦄ ⊢ ⬊*[h, o] T1 →
+                      ∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, o] T2 → ⦃G, L⦄ ⊢ ⬊*[h, o] T2.
+#h #o #G #L #T1 #HT1 #T2 #H @(cpxs_ind … H) -T2 /2 width=3 by csx_cpx_trans/
 qed-.
 
 (* Main eliminators *********************************************************)
 
-lemma csx_ind_alt: ∀h,g,G,L. ∀R:predicate term.
-                   (∀T1. ⦃G, L⦄ ⊢ ⬊*[h, g] T1 →
-                         (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → (T1 = T2 → ⊥) → R T2) → R T1
+lemma csx_ind_alt: ∀h,o,G,L. ∀R:predicate term.
+                   (∀T1. ⦃G, L⦄ ⊢ ⬊*[h, o] T1 →
+                         (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, o] T2 → (T1 = T2 → ⊥) → R T2) → R T1
                    ) →
-                   ∀T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → R T.
-#h #g #G #L #R #H0 #T1 #H @(csxa_ind … (csx_csxa … H)) -T1 /4 width=1 by csxa_csx/
+                   ∀T. ⦃G, L⦄ ⊢ ⬊*[h, o] T → R T.
+#h #o #G #L #R #H0 #T1 #H @(csxa_ind … (csx_csxa … H)) -T1 /4 width=1 by csxa_csx/
 qed-.