- new extendedd beta-reductum involving native type annotation

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cprs.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cprs.ma
index d3aaae5deb2e4c272c1b68032d9c9293bbaba27a..c0e440d69bbc70c80b488ebb4f461139582c4780 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/cprs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cprs.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/reduction/cnf.ma".
+include "basic_2/reduction/cnr.ma".
 
 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
 
@@ -66,8 +66,8 @@ lemma cprs_cpss_trans: ∀L,T1,T. L ⊢ T1 ➡* T → ∀T2. L ⊢ T ▶* T2 →
 lemma cpss_cprs_trans: ∀L,T1,T. L ⊢ T1 ▶* T → ∀T2. L ⊢ T ➡* T2 → L ⊢ T1 ➡* T2.
 /3 width=3/ qed-.
 
-lemma cprs_lsubr_trans: lsubr_trans … cprs.
-/3 width=3 by cpr_lsubr_trans, TC_lsubr_trans/
+lemma cprs_lsubr_trans: lsub_trans … cprs lsubr.
+/3 width=5 by cpr_lsubr_trans, TC_lsub_trans/
 qed-.
 
 (* Basic_1: was: pr3_pr1 *)
@@ -114,18 +114,15 @@ qed.
 lemma cprs_beta_dx: ∀a,L,V1,V2,W,T1,T2.
                     L ⊢ V1 ➡ V2 → L.ⓛW ⊢ T1 ➡* T2 →
                     L ⊢ ⓐV1.ⓛ{a}W.T1 ➡* ⓓ{a}V2.T2.
-#a #L #V1 #V2 #W #T1 #T2 #HV12 #H elim H -T2 /3 width=1/
-#T #T2 #_ #HT2 #IHT1
-@(cprs_strap1 … IHT1) -V1 -T1 /3 width=2/
+#a #L #V1 #V2 #W #T1 #T2 #HV12 * -T2 /3 width=1/
+/4 width=6 by cprs_strap1, cprs_bind_dx, cprs_flat_dx, cpr_beta/ (**) (* auto too slow without trace *)
 qed.
 
-lemma cprs_theta_dx: ∀a,L,V1,V,V2,W1,T1,T2.
+lemma cprs_theta_dx: ∀a,L,V1,V,V2,W1,W2,T1,T2.
                      L ⊢ V1 ➡ V → ⇧[0, 1] V ≡ V2 → L.ⓓW1 ⊢ T1 ➡* T2 →
-                     ∀W2. L ⊢ W1 ➡ W2 → L ⊢ ⓐV1.ⓓ{a}W1.T1 ➡* ⓓ{a}W2.ⓐV2.T2.
-#a #L #V1 #V #V2 #W1 #T1 #T2 #HV1 #HV2 #H elim H -T2 [ /3 width=3/ ]
-#T #T2 #_ #HT2 #IHT1 #W2 #HW12
-lapply (IHT1 W1 ?) -IHT1 // #HT1
-@(cprs_strap1 … HT1) -HT1 -V -V1 /3 width=1/
+                     L ⊢ W1 ➡ W2 → L ⊢ ⓐV1.ⓓ{a}W1.T1 ➡* ⓓ{a}W2.ⓐV2.T2.
+#a #L #V1 #V #V2 #W1 #W2 #T1 #T2 #HV1 #HV2 * -T2 [ /3 width=3/ ]
+/4 width=9 by cprs_strap1, cprs_bind_dx, cprs_flat_dx, cpr_theta/ (**) (* auto too slow without trace *)
 qed.
 
 (* Basic inversion lemmas ***************************************************)
@@ -171,7 +168,7 @@ elim (cpr_inv_cast1 … HU2) -HU2 /3 width=3/ *
 qed-.
 
 (* Basic_1: was: nf2_pr3_unfold *)
-lemma cprs_inv_cnf1: ∀L,T,U. L ⊢ T ➡* U → L ⊢ 𝐍⦃T⦄ → T = U.
+lemma cprs_inv_cnr1: ∀L,T,U. L ⊢ T ➡* U → L ⊢ 𝐍⦃T⦄ → T = U.
 #L #T #U #H @(cprs_ind_dx … H) -T //
 #T0 #T #H1T0 #_ #IHT #H2T0
 lapply (H2T0 … H1T0) -H1T0 #H destruct /2 width=1/