X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fcomputation%2Fcprs.ma;h=45c8cfe7dddd88c5ab0f36be5360c9fa152ec825;hb=606dab57f31b66eb3f30f603185124b88dfad4c1;hp=640f4dbfce2192b8a6a3feb6ef0dd923f875aeaf;hpb=946abd88fa24966751555193b0fe0d52e50722f2;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cprs.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cprs.ma
index 640f4dbfc..45c8cfe7d 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/cprs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cprs.ma
@@ -44,20 +44,20 @@ qed-.
 
 (* Basic_1: was: pr3_pr2 *)
 lemma cpr_cprs: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 → ⦃G, L⦄ ⊢ T1 ➡* T2.
-/2 width=1/ qed.
+/2 width=1 by inj/ qed.
 
 (* Basic_1: was: pr3_refl *)
 lemma cprs_refl: ∀G,L,T. ⦃G, L⦄ ⊢ T ➡* T.
-/2 width=1/ qed.
+/2 width=1 by cpr_cprs/ qed.
 
 lemma cprs_strap1: ∀G,L,T1,T,T2.
                    ⦃G, L⦄ ⊢ T1 ➡* T → ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T1 ➡* T2.
-normalize /2 width=3/ qed.
+normalize /2 width=3 by step/ qed.
 
 (* Basic_1: was: pr3_step *)
 lemma cprs_strap2: ∀G,L,T1,T,T2.
                    ⦃G, L⦄ ⊢ T1 ➡ T → ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 ➡* T2.
-normalize /2 width=3/ qed.
+normalize /2 width=3 by TC_strap/ qed.
 
 lemma lsubr_cprs_trans: ∀G. lsub_trans … (cprs G) lsubr.
 /3 width=5 by lsubr_cpr_trans, LTC_lsub_trans/
@@ -65,51 +65,49 @@ qed-.
 
 (* Basic_1: was: pr3_pr1 *)
 lemma tprs_cprs: ∀G,L,T1,T2. ⦃G, ⋆⦄ ⊢ T1 ➡* T2 → ⦃G, L⦄ ⊢ T1 ➡* T2.
-#G #L #T1 #T2 #H @(lsubr_cprs_trans … H) -H //
-qed.
+/2 width=3 by lsubr_cprs_trans/ qed.
 
 lemma cprs_bind_dx: ∀G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡ V2 → ∀I,T1,T2. ⦃G, L.ⓑ{I}V1⦄ ⊢ T1 ➡* T2 →
                     ∀a. ⦃G, L⦄ ⊢ ⓑ{a,I}V1. T1 ➡* ⓑ{a,I}V2. T2.
 #G #L #V1 #V2 #HV12 #I #T1 #T2 #HT12 #a @(cprs_ind_dx … HT12) -T1
-/3 width=1/ /3 width=3/
-qed.
+/3 width=3 by cprs_strap2, cpr_cprs, cpr_pair_sn, cpr_bind/ qed.
 
 (* Basic_1: was only: pr3_thin_dx *)
 lemma cprs_flat_dx: ∀I,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡ V2 → ∀T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 →
                     ⦃G, L⦄ ⊢ ⓕ{I} V1. T1 ➡* ⓕ{I} V2. T2.
-#I #G #L #V1 #V2 #HV12 #T1 #T2 #HT12 @(cprs_ind … HT12) -T2 /3 width=1/
-#T #T2 #_ #HT2 #IHT1
-@(cprs_strap1 … IHT1) -V1 -T1 /2 width=1/
+#I #G #L #V1 #V2 #HV12 #T1 #T2 #HT12 @(cprs_ind … HT12) -T2
+/3 width=5 by cprs_strap1, cpr_flat, cpr_cprs, cpr_pair_sn/
 qed.
 
 lemma cprs_flat_sn: ∀I,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 → ∀V1,V2. ⦃G, L⦄ ⊢ V1 ➡* V2 →
                     ⦃G, L⦄ ⊢ ⓕ{I} V1. T1 ➡* ⓕ{I} V2. T2.
-#I #G #L #T1 #T2 #HT12 #V1 #V2 #H @(cprs_ind … H) -V2 /3 width=1/
-#V #V2 #_ #HV2 #IHV1
-@(cprs_strap1 … IHV1) -V1 -T1 /2 width=1/
+#I #G #L #T1 #T2 #HT12 #V1 #V2 #H @(cprs_ind … H) -V2
+/3 width=3 by cprs_strap1, cpr_cprs, cpr_pair_sn, cpr_flat/
 qed.
 
 lemma cprs_zeta: ∀G,L,V,T1,T,T2. ⇧[0, 1] T2 ≡ T →
                  ⦃G, L.ⓓV⦄ ⊢ T1 ➡* T → ⦃G, L⦄ ⊢ +ⓓV.T1 ➡* T2.
-#G #L #V #T1 #T #T2 #HT2 #H @(TC_ind_dx … T1 H) -T1 /3 width=3/
+#G #L #V #T1 #T #T2 #HT2 #H @(cprs_ind_dx … H) -T1
+/3 width=3 by cprs_strap2, cpr_cprs, cpr_bind, cpr_zeta/
 qed.
 
 lemma cprs_tau: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → ∀V. ⦃G, L⦄ ⊢ ⓝV.T1 ➡* T2.
-#G #L #T1 #T2 #H elim H -T2 /2 width=3/ /3 width=1/
+#G #L #T1 #T2 #H @(cprs_ind … H) -T2
+/3 width=3 by cprs_strap1, cpr_cprs, cpr_tau/
 qed.
 
 lemma cprs_beta_dx: ∀a,G,L,V1,V2,W1,W2,T1,T2.
                     ⦃G, L⦄ ⊢ V1 ➡ V2 → ⦃G, L⦄ ⊢ W1 ➡ W2 → ⦃G, L.ⓛW1⦄ ⊢ T1 ➡* T2 →
                     ⦃G, L⦄ ⊢ ⓐV1.ⓛ{a}W1.T1 ➡* ⓓ{a}ⓝW2.V2.T2.
-#a #G #L #V1 #V2 #W1 #W2 #T1 #T2 #HV12 #HW12 * -T2 /3 width=1/
-/4 width=7 by cprs_strap1, cprs_bind_dx, cprs_flat_dx, cpr_beta/ (**) (* auto too slow without trace *)
+#a #G #L #V1 #V2 #W1 #W2 #T1 #T2 #HV12 #HW12 * -T2
+/4 width=7 by cprs_strap1, cpr_cprs, cprs_bind_dx, cprs_flat_dx, cpr_beta/
 qed.
 
 lemma cprs_theta_dx: ∀a,G,L,V1,V,V2,W1,W2,T1,T2.
                      ⦃G, L⦄ ⊢ V1 ➡ V → ⇧[0, 1] V ≡ V2 → ⦃G, L.ⓓW1⦄ ⊢ T1 ➡* T2 →
                      ⦃G, L⦄ ⊢ W1 ➡ W2 → ⦃G, L⦄ ⊢ ⓐV1.ⓓ{a}W1.T1 ➡* ⓓ{a}W2.ⓐV2.T2.
-#a #G #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 *)
+#a #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 #HV1 #HV2 * -T2
+/4 width=9 by cprs_strap1, cpr_cprs, cprs_bind_dx, cprs_flat_dx, cpr_theta/
 qed.
 
 (* Basic inversion lemmas ***************************************************)
@@ -125,17 +123,17 @@ qed-.
 lemma cprs_inv_cast1: ∀G,L,W1,T1,U2. ⦃G, L⦄ ⊢ ⓝW1.T1 ➡* U2 → ⦃G, L⦄ ⊢ T1 ➡* U2 ∨
                       ∃∃W2,T2. ⦃G, L⦄ ⊢ W1 ➡* W2 & ⦃G, L⦄ ⊢ T1 ➡* T2 & U2 = ⓝW2.T2.
 #G #L #W1 #T1 #U2 #H @(cprs_ind … H) -U2 /3 width=5/
-#U2 #U #_ #HU2 * /3 width=3/ *
+#U2 #U #_ #HU2 * /3 width=3 by cprs_strap1, or_introl/ *
 #W #T #HW1 #HT1 #H destruct
-elim (cpr_inv_cast1 … HU2) -HU2 /3 width=3/ *
-#W2 #T2 #HW2 #HT2 #H destruct /4 width=5/
+elim (cpr_inv_cast1 … HU2) -HU2 /3 width=3 by cprs_strap1, or_introl/ *
+#W2 #T2 #HW2 #HT2 #H destruct /4 width=5 by cprs_strap1, ex3_2_intro, or_intror/
 qed-.
 
 (* Basic_1: was: nf2_pr3_unfold *)
-lemma cprs_inv_cnr1: ∀G,L,T,U. ⦃G, L⦄ ⊢ T ➡* U → ⦃G, L⦄ ⊢ 𝐍⦃T⦄ → T = U.
+lemma cprs_inv_cnr1: ∀G,L,T,U. ⦃G, L⦄ ⊢ T ➡* U → ⦃G, L⦄ ⊢ ➡ 𝐍⦃T⦄ → T = U.
 #G #L #T #U #H @(cprs_ind_dx … H) -T //
 #T0 #T #H1T0 #_ #IHT #H2T0
-lapply (H2T0 … H1T0) -H1T0 #H destruct /2 width=1/
+lapply (H2T0 … H1T0) -H1T0 #H destruct /2 width=1 by/
 qed-.
 
 (* Basic_1: removed theorems 13: