partial commit: "computation" component ...

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_cpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_cpxs.ma
index 8958323296e1c68538e3f96df123682204ebdaef..f25909b757436e51a8b667bfd6c4ec42d0c2d56a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_cpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_cpxs.ma
@@ -12,75 +12,75 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/reduction/lpx_ldrop.ma".
 include "basic_2/computation/cpxs_lift.ma".
+include "basic_2/reduction/lpx_ldrop.ma". (**) (* disambiguation error *)
 
 (* CONTEXT-SENSITIVE EXTENDED PARALLEL COMPUTATION ON TERMS *****************)
 
 (* Main properties **********************************************************)
 
-theorem cpxs_trans: ∀h,g,L. Transitive … (cpxs h g L).
-#h #g #L #T1 #T #HT1 #T2 @trans_TC @HT1 qed-. (**) (* auto /3 width=3/ does not work because a δ-expansion gets in the way *)
+theorem cpxs_trans: ∀h,g,G,L. Transitive … (cpxs h g G L).
+#h #g #G #L #T1 #T #HT1 #T2 @trans_TC @HT1 qed-. (**) (* auto /3 width=3/ does not work because a δ-expansion gets in the way *)
 
-theorem cpxs_bind: ∀h,g,a,I,L,V1,V2,T1,T2. ⦃h, L.ⓑ{I}V1⦄ ⊢ T1 ➡*[h, g] T2 →
+theorem cpxs_bind: ∀h,g,a,I,G,L,V1,V2,T1,T2. ⦃G, L.ⓑ{I}V1⦄ ⊢ T1 ➡*[h, g] T2 →
                    ⦃G, L⦄ ⊢ V1 ➡*[h, g] V2 →
                    ⦃G, L⦄ ⊢ ⓑ{a,I}V1.T1 ➡*[h, g] ⓑ{a,I}V2.T2.
-#h #g #a #I #L #V1 #V2 #T1 #T2 #HT12 #H @(cpxs_ind … H) -V2 /2 width=1/
+#h #g #a #I #G #L #V1 #V2 #T1 #T2 #HT12 #H @(cpxs_ind … H) -V2 /2 width=1/
 #V #V2 #_ #HV2 #IHV1
 @(cpxs_trans … IHV1) -V1 /2 width=1/
 qed.
 
-theorem cpxs_flat: ∀h,g,I,L,V1,V2,T1,T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 →
+theorem cpxs_flat: ∀h,g,I,G,L,V1,V2,T1,T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 →
                    ⦃G, L⦄ ⊢ V1 ➡*[h, g] V2 →
-                   ⦃G, L⦄ ⊢ ⓕ{I} V1.T1 ➡*[h, g] ⓕ{I} V2.T2.
-#h #g #I #L #V1 #V2 #T1 #T2 #HT12 #H @(cpxs_ind … H) -V2 /2 width=1/
+                   ⦃G, L⦄ ⊢ ⓕ{I}V1.T1 ➡*[h, g] ⓕ{I}V2.T2.
+#h #g #I #G #L #V1 #V2 #T1 #T2 #HT12 #H @(cpxs_ind … H) -V2 /2 width=1/
 #V #V2 #_ #HV2 #IHV1
 @(cpxs_trans … IHV1) -IHV1 /2 width=1/
 qed.
 
-theorem cpxs_beta_rc: ∀h,g,a,L,V1,V2,W1,W2,T1,T2.
-                      ⦃G, L⦄ ⊢ V1 ➡[h, g] V2 → ⦃h, L.ⓛW1⦄ ⊢ T1 ➡*[h, g] T2 → ⦃G, L⦄ ⊢ W1 ➡*[h, g] W2 →
+theorem cpxs_beta_rc: ∀h,g,a,G,L,V1,V2,W1,W2,T1,T2.
+                      ⦃G, L⦄ ⊢ V1 ➡[h, g] V2 → ⦃G, L.ⓛW1⦄ ⊢ T1 ➡*[h, g] T2 → ⦃G, L⦄ ⊢ W1 ➡*[h, g] W2 →
                       ⦃G, L⦄ ⊢ ⓐV1.ⓛ{a}W1.T1 ➡*[h, g] ⓓ{a}ⓝW2.V2.T2.
-#h #g #a #L #V1 #V2 #W1 #W2 #T1 #T2 #HV12 #HT12 #H @(cpxs_ind … H) -W2 /2 width=1/
+#h #g #a #G #L #V1 #V2 #W1 #W2 #T1 #T2 #HV12 #HT12 #H @(cpxs_ind … H) -W2 /2 width=1/
 #W #W2 #_ #HW2 #IHW1
 @(cpxs_trans … IHW1) -IHW1 /3 width=1/
 qed.
 
-theorem cpxs_beta: ∀h,g,a,L,V1,V2,W1,W2,T1,T2.
-                   ⦃h, L.ⓛW1⦄ ⊢ T1 ➡*[h, g] T2 → ⦃G, L⦄ ⊢ W1 ➡*[h, g] W2 → ⦃G, L⦄ ⊢ V1 ➡*[h, g] V2 →
+theorem cpxs_beta: ∀h,g,a,G,L,V1,V2,W1,W2,T1,T2.
+                   ⦃G, L.ⓛW1⦄ ⊢ T1 ➡*[h, g] T2 → ⦃G, L⦄ ⊢ W1 ➡*[h, g] W2 → ⦃G, L⦄ ⊢ V1 ➡*[h, g] V2 →
                    ⦃G, L⦄ ⊢ ⓐV1.ⓛ{a}W1.T1 ➡*[h, g] ⓓ{a}ⓝW2.V2.T2.
-#h #g #a #L #V1 #V2 #W1 #W2 #T1 #T2 #HT12 #HW12 #H @(cpxs_ind … H) -V2 /2 width=1/
+#h #g #a #G #L #V1 #V2 #W1 #W2 #T1 #T2 #HT12 #HW12 #H @(cpxs_ind … H) -V2 /2 width=1/
 #V #V2 #_ #HV2 #IHV1
 @(cpxs_trans … IHV1) -IHV1 /3 width=1/
 qed.
 
-theorem cpxs_theta_rc: ∀h,g,a,L,V1,V,V2,W1,W2,T1,T2.
+theorem cpxs_theta_rc: ∀h,g,a,G,L,V1,V,V2,W1,W2,T1,T2.
                        ⦃G, L⦄ ⊢ V1 ➡[h, g] V → ⇧[0, 1] V ≡ V2 →
-                       ⦃h, L.ⓓW1⦄ ⊢ T1 ➡*[h, g] T2 → ⦃G, L⦄ ⊢ W1 ➡*[h, g] W2 →
+                       ⦃G, L.ⓓW1⦄ ⊢ T1 ➡*[h, g] T2 → ⦃G, L⦄ ⊢ W1 ➡*[h, g] W2 →
                        ⦃G, L⦄ ⊢ ⓐV1.ⓓ{a}W1.T1 ➡*[h, g] ⓓ{a}W2.ⓐV2.T2.
-#h #g #a #L #V1 #V #V2 #W1 #W2 #T1 #T2 #HV1 #HV2 #HT12 #H elim H -W2 /2 width=3/
+#h #g #a #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 #HV1 #HV2 #HT12 #H elim H -W2 /2 width=3/
 #W #W2 #_ #HW2 #IHW1
 @(cpxs_trans … IHW1) -IHW1 /2 width=1/
 qed.
 
-theorem cpxs_theta: ∀h,g,a,L,V1,V,V2,W1,W2,T1,T2.
+theorem cpxs_theta: ∀h,g,a,G,L,V1,V,V2,W1,W2,T1,T2.
                     ⇧[0, 1] V ≡ V2 → ⦃G, L⦄ ⊢ W1 ➡*[h, g] W2 →
-                    ⦃h, L.ⓓW1⦄ ⊢ T1 ➡*[h, g] T2 → ⦃G, L⦄ ⊢ V1 ➡*[h, g] V →
+                    ⦃G, L.ⓓW1⦄ ⊢ T1 ➡*[h, g] T2 → ⦃G, L⦄ ⊢ V1 ➡*[h, g] V →
                     ⦃G, L⦄ ⊢ ⓐV1.ⓓ{a}W1.T1 ➡*[h, g] ⓓ{a}W2.ⓐV2.T2.
-#h #g #a #L #V1 #V #V2 #W1 #W2 #T1 #T2 #HV2 #HW12 #HT12 #H @(TC_ind_dx … V1 H) -V1 /2 width=3/
+#h #g #a #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 #HV2 #HW12 #HT12 #H @(TC_ind_dx … V1 H) -V1 /2 width=3/
 #V1 #V0 #HV10 #_ #IHV0
 @(cpxs_trans … IHV0) -IHV0 /2 width=1/
 qed.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma cpxs_inv_appl1: ∀h,g,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓐV1.T1 ➡*[h, g] U2 →
+lemma cpxs_inv_appl1: ∀h,g,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓐV1.T1 ➡*[h, g] U2 →
                       ∨∨ ∃∃V2,T2.       ⦃G, L⦄ ⊢ V1 ➡*[h, g] V2 & ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 &
                                         U2 = ⓐV2. T2
                        | ∃∃a,W,T.       ⦃G, L⦄ ⊢ T1 ➡*[h, g] ⓛ{a}W.T & ⦃G, L⦄ ⊢ ⓓ{a}ⓝW.V1.T ➡*[h, g] U2
                        | ∃∃a,V0,V2,V,T. ⦃G, L⦄ ⊢ V1 ➡*[h, g] V0 & ⇧[0,1] V0 ≡ V2 &
                                         ⦃G, L⦄ ⊢ T1 ➡*[h, g] ⓓ{a}V.T & ⦃G, L⦄ ⊢ ⓓ{a}V.ⓐV2.T ➡*[h, g] U2.
-#h #g #L #V1 #T1 #U2 #H @(cpxs_ind … H) -U2 [ /3 width=5/ ]
+#h #g #G #L #V1 #T1 #U2 #H @(cpxs_ind … H) -U2 [ /3 width=5/ ]
 #U #U2 #_ #HU2 * *
 [ #V0 #T0 #HV10 #HT10 #H destruct
   elim (cpx_inv_appl1 … HU2) -HU2 *
@@ -99,42 +99,42 @@ qed-.
 
 (* Properties on sn extended parallel reduction for local environments ******)
 
-lemma lpx_cpx_trans: ∀h,g. s_r_trans … (cpx h g) (lpx h g).
-#h #g #L2 #T1 #T2 #HT12 elim HT12 -L2 -T1 -T2
+lemma lpx_cpx_trans: ∀h,g,G. s_r_trans … (cpx h g G) (lpx h g G).
+#h #g #G #L2 #T1 #T2 #HT12 elim HT12 -G -L2 -T1 -T2
 [ /2 width=3/
 | /3 width=2/
-| #I #L2 #K2 #V0 #V2 #W2 #i #HLK2 #_ #HVW2 #IHV02 #L1 #HL12
+| #I #G #L2 #K2 #V0 #V2 #W2 #i #HLK2 #_ #HVW2 #IHV02 #L1 #HL12
   elim (lpx_ldrop_trans_O1 … HL12 … HLK2) -L2 #X #HLK1 #H
   elim (lpx_inv_pair2 … H) -H #K1 #V1 #HK12 #HV10 #H destruct
   lapply (IHV02 … HK12) -K2 #HV02
   lapply (cpxs_strap2 … HV10 … HV02) -V0 /2 width=7/
-| #a #I #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #HL12
+| #a #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #HL12
   lapply (IHT12 (L1.ⓑ{I}V1) ?) -IHT12 /2 width=1/ /3 width=1/
 |5,7,8: /3 width=1/
-| #L2 #V2 #T1 #T #T2 #_ #HT2 #IHT1 #L1 #HL12
+| #G #L2 #V2 #T1 #T #T2 #_ #HT2 #IHT1 #L1 #HL12
   lapply (IHT1 (L1.ⓓV2) ?) -IHT1 /2 width=1/ /2 width=3/
-| #a #L2 #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #L1 #HL12
+| #a #G #L2 #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #L1 #HL12
   lapply (IHT12 (L1.ⓛW1) ?) -IHT12 /2 width=1/ /3 width=1/
-| #a #L2 #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV1 #IHW12 #IHT12 #L1 #HL12
+| #a #G #L2 #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV1 #IHW12 #IHT12 #L1 #HL12
   lapply (IHT12 (L1.ⓓW1) ?) -IHT12 /2 width=1/ /3 width=3/
 ]
 qed-.
 
-lemma cpx_bind2: ∀h,g,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡[h, g] V2 →
-                 ∀I,T1,T2. ⦃h, L.ⓑ{I}V2⦄ ⊢ T1 ➡[h, g] T2 →
+lemma cpx_bind2: ∀h,g,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡[h, g] V2 →
+                 ∀I,T1,T2. ⦃G, L.ⓑ{I}V2⦄ ⊢ T1 ➡[h, g] T2 →
                  ∀a. ⦃G, L⦄ ⊢ ⓑ{a,I}V1.T1 ➡*[h, g] ⓑ{a,I}V2.T2.
-#h #g #L #V1 #V2 #HV12 #I #T1 #T2 #HT12
+#h #g #G #L #V1 #V2 #HV12 #I #T1 #T2 #HT12
 lapply (lpx_cpx_trans … HT12 (L.ⓑ{I}V1) ?) /2 width=1/
 qed.
 
 (* Advanced properties ******************************************************)
 
-lemma lpx_cpxs_trans: ∀h,g. s_rs_trans … (cpx h g) (lpx h g).
+lemma lpx_cpxs_trans: ∀h,g,G. s_rs_trans … (cpx h g G) (lpx h g G).
 /3 width=5 by s_r_trans_TC1, lpx_cpx_trans/ qed-.
 
-lemma cpxs_bind2_dx: ∀h,g,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡[h, g] V2 →
-                     ∀I,T1,T2. ⦃h, L.ⓑ{I}V2⦄ ⊢ T1 ➡*[h, g] T2 →
+lemma cpxs_bind2_dx: ∀h,g,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡[h, g] V2 →
+                     ∀I,T1,T2. ⦃G, L.ⓑ{I}V2⦄ ⊢ T1 ➡*[h, g] T2 →
                      ∀a. ⦃G, L⦄ ⊢ ⓑ{a,I}V1.T1 ➡*[h, g] ⓑ{a,I}V2.T2.
-#h #g #L #V1 #V2 #HV12 #I #T1 #T2 #HT12
+#h #g #G #L #V1 #V2 #HV12 #I #T1 #T2 #HT12
 lapply (lpx_cpxs_trans … HT12 (L.ⓑ{I}V1) ?) /2 width=1/
 qed.