- commit of the "s_computation" component ...

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/csx_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/csx_lift.ma
index fabd9b1b9820460699f892e967a0ba5c4b7012b0..354b59a213be0881ef5a4744bdfdb0499addf265 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/csx_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/csx_lift.ma
@@ -21,9 +21,9 @@ include "basic_2/computation/csx.ma".
 (* Relocation properties ****************************************************)
 
 (* Basic_1: was just: sn3_lift *)
-lemma csx_lift: ∀h,g,G,L2,L1,T1,s,l,m. ⦃G, L1⦄ ⊢ ⬊*[h, g] T1 →
-                ∀T2. ⬇[s, l, m] L2 ≡ L1 → ⬆[l, m] T1 ≡ T2 → ⦃G, L2⦄ ⊢ ⬊*[h, g] T2.
-#h #g #G #L2 #L1 #T1 #s #l #m #H elim H -T1 #T1 #_ #IHT1 #T2 #HL21 #HT12
+lemma csx_lift: ∀h,o,G,L2,L1,T1,c,l,k. ⦃G, L1⦄ ⊢ ⬊*[h, o] T1 →
+                ∀T2. ⬇[c, l, k] L2 ≡ L1 → ⬆[l, k] T1 ≡ T2 → ⦃G, L2⦄ ⊢ ⬊*[h, o] T2.
+#h #o #G #L2 #L1 #T1 #c #l #k #H elim H -T1 #T1 #_ #IHT1 #T2 #HL21 #HT12
 @csx_intro #T #HLT2 #HT2
 elim (cpx_inv_lift1 … HLT2 … HL21 … HT12) -HLT2 #T0 #HT0 #HLT10
 @(IHT1 … HLT10) // -L1 -L2 #H destruct
@@ -31,11 +31,11 @@ elim (cpx_inv_lift1 … HLT2 … HL21 … HT12) -HLT2 #T0 #HT0 #HLT10
 qed.
 
 (* Basic_1: was just: sn3_gen_lift *)
-lemma csx_inv_lift: ∀h,g,G,L2,L1,T1,s,l,m. ⦃G, L1⦄ ⊢ ⬊*[h, g] T1 →
-                    ∀T2. ⬇[s, l, m] L1 ≡ L2 → ⬆[l, m] T2 ≡ T1 → ⦃G, L2⦄ ⊢ ⬊*[h, g] T2.
-#h #g #G #L2 #L1 #T1 #s #l #m #H elim H -T1 #T1 #_ #IHT1 #T2 #HL12 #HT21
+lemma csx_inv_lift: ∀h,o,G,L2,L1,T1,c,l,k. ⦃G, L1⦄ ⊢ ⬊*[h, o] T1 →
+                    ∀T2. ⬇[c, l, k] L1 ≡ L2 → ⬆[l, k] T2 ≡ T1 → ⦃G, L2⦄ ⊢ ⬊*[h, o] T2.
+#h #o #G #L2 #L1 #T1 #c #l #k #H elim H -T1 #T1 #_ #IHT1 #T2 #HL12 #HT21
 @csx_intro #T #HLT2 #HT2
-elim (lift_total T l m) #T0 #HT0
+elim (lift_total T l k) #T0 #HT0
 lapply (cpx_lift … HLT2 … HL12 … HT21 … HT0) -HLT2 #HLT10
 @(IHT1 … HLT10) // -L1 -L2 #H destruct
 >(lift_inj … HT0 … HT21) in HT2; -T1 /2 width=1 by/
@@ -44,9 +44,9 @@ qed.
 (* Advanced inversion lemmas ************************************************)
 
 (* Basic_1: was: sn3_gen_def *)
-lemma csx_inv_lref_bind: ∀h,g,I,G,L,K,V,i. ⬇[i] L ≡ K.ⓑ{I}V →
-                         ⦃G, L⦄ ⊢ ⬊*[h, g] #i → ⦃G, K⦄ ⊢ ⬊*[h, g] V.
-#h #g #I #G #L #K #V #i #HLK #Hi
+lemma csx_inv_lref_bind: ∀h,o,I,G,L,K,V,i. ⬇[i] L ≡ K.ⓑ{I}V →
+                         ⦃G, L⦄ ⊢ ⬊*[h, o] #i → ⦃G, K⦄ ⊢ ⬊*[h, o] V.
+#h #o #I #G #L #K #V #i #HLK #Hi
 elim (lift_total V 0 (i+1))
 /4 width=9 by csx_inv_lift, csx_cpx_trans, cpx_delta, drop_fwd_drop2/
 qed-.
@@ -54,8 +54,8 @@ qed-.
 (* Advanced properties ******************************************************)
 
 (* Basic_1: was just: sn3_abbr *)
-lemma csx_lref_bind: ∀h,g,I,G,L,K,V,i. ⬇[i] L ≡ K.ⓑ{I}V → ⦃G, K⦄ ⊢ ⬊*[h, g] V → ⦃G, L⦄ ⊢ ⬊*[h, g] #i.
-#h #g #I #G #L #K #V #i #HLK #HV
+lemma csx_lref_bind: ∀h,o,I,G,L,K,V,i. ⬇[i] L ≡ K.ⓑ{I}V → ⦃G, K⦄ ⊢ ⬊*[h, o] V → ⦃G, L⦄ ⊢ ⬊*[h, o] #i.
+#h #o #I #G #L #K #V #i #HLK #HV
 @csx_intro #X #H #Hi
 elim (cpx_inv_lref1 … H) -H
 [ #H destruct elim Hi //
@@ -65,10 +65,10 @@ elim (cpx_inv_lref1 … H) -H
 ]
 qed.
 
-lemma csx_appl_simple: ∀h,g,G,L,V. ⦃G, L⦄ ⊢ ⬊*[h, g] V → ∀T1.
-                       (∀T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 → (T1 = T2 → ⊥) → ⦃G, L⦄ ⊢ ⬊*[h, g] ⓐV.T2) →
-                       𝐒⦃T1⦄ → ⦃G, L⦄ ⊢ ⬊*[h, g] ⓐV.T1.
-#h #g #G #L #V #H @(csx_ind … H) -V #V #_ #IHV #T1 #IHT1 #HT1
+lemma csx_appl_simple: ∀h,o,G,L,V. ⦃G, L⦄ ⊢ ⬊*[h, o] V → ∀T1.
+                       (∀T2. ⦃G, L⦄ ⊢ T1 ➡[h, o] T2 → (T1 = T2 → ⊥) → ⦃G, L⦄ ⊢ ⬊*[h, o] ⓐV.T2) →
+                       𝐒⦃T1⦄ → ⦃G, L⦄ ⊢ ⬊*[h, o] ⓐV.T1.
+#h #o #G #L #V #H @(csx_ind … H) -V #V #_ #IHV #T1 #IHT1 #HT1
 @csx_intro #X #H1 #H2
 elim (cpx_inv_appl1_simple … H1) // -H1
 #V0 #T0 #HLV0 #HLT10 #H destruct
@@ -79,29 +79,29 @@ elim (eq_false_inv_tpair_dx … H2) -H2
 ]
 qed.
 
-lemma csx_fqu_conf: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
-                    ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 → ⦃G2, L2⦄ ⊢ ⬊*[h, g] T2.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
+lemma csx_fqu_conf: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
+                    ⦃G1, L1⦄ ⊢ ⬊*[h, o] T1 → ⦃G2, L2⦄ ⊢ ⬊*[h, o] T2.
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
 /2 width=8 by csx_inv_lref_bind, csx_inv_lift, csx_fwd_flat_dx, csx_fwd_bind_dx, csx_fwd_pair_sn/
 qed-.
 
-lemma csx_fquq_conf: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
-                     ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 → ⦃G2, L2⦄ ⊢ ⬊*[h, g] T2.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H12 #H elim (fquq_inv_gen … H12) -H12
+lemma csx_fquq_conf: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
+                     ⦃G1, L1⦄ ⊢ ⬊*[h, o] T1 → ⦃G2, L2⦄ ⊢ ⬊*[h, o] T2.
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H12 #H elim (fquq_inv_gen … H12) -H12
 [ /2 width=5 by csx_fqu_conf/
 | * #HG #HL #HT destruct //
 ]
 qed-.
 
-lemma csx_fqup_conf: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ →
-                     ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 → ⦃G2, L2⦄ ⊢ ⬊*[h, g] T2.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
+lemma csx_fqup_conf: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ →
+                     ⦃G1, L1⦄ ⊢ ⬊*[h, o] T1 → ⦃G2, L2⦄ ⊢ ⬊*[h, o] T2.
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
 /3 width=5 by csx_fqu_conf/
 qed-.
 
-lemma csx_fqus_conf: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
-                     ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 → ⦃G2, L2⦄ ⊢ ⬊*[h, g] T2.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H12 #H elim (fqus_inv_gen … H12) -H12
+lemma csx_fqus_conf: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
+                     ⦃G1, L1⦄ ⊢ ⬊*[h, o] T1 → ⦃G2, L2⦄ ⊢ ⬊*[h, o] T2.
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H12 #H elim (fqus_inv_gen … H12) -H12
 [ /2 width=5 by csx_fqup_conf/
 | * #HG #HL #HT destruct //
 ]
@@ -109,10 +109,10 @@ qed-.
 
 (* Main properties **********************************************************)
 
-theorem csx_gcp: ∀h,g. gcp (cpx h g) (eq …) (csx h g).
-#h #g @mk_gcp
+theorem csx_gcp: ∀h,o. gcp (cpx h o) (eq …) (csx h o).
+#h #o @mk_gcp
 [ normalize /3 width=13 by cnx_lift/
-| #G #L elim (deg_total h g 0) /3 width=8 by cnx_sort_iter, ex_intro/
+| #G #L elim (deg_total h o 0) /3 width=8 by cnx_sort_iter, ex_intro/
 | /2 width=8 by csx_lift/
 | /2 width=3 by csx_fwd_flat_dx/
 ]