- degree assignment, static type assignment, iterated static type

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / snv_aaa.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_aaa.ma
index 6a823189a26feea6a7c98b527eb740085b6e7e1b..e55dd6888cd71e4a6a60fe9a796f20b3f2f2c0bd 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_aaa.ma
@@ -26,16 +26,41 @@ lemma snv_fwd_aaa: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] → ∃A. ⦃G, L⦄
 [ /2 width=2/
 | #I #G #L #K #V #i #HLK #_ * /3 width=6/
 | #a * #G #L #V #T #_ #_ * #B #HV * #A #HA /3 width=2/
-| #a #G #L #V #W #W0 #T #U #l #_ #_ #HVW #HW0 #HTU * #B #HV * #X #HT
-  lapply (cpds_aaa h g … HV W0 ?) [ -HTU /3 width=4/ ] -W #HW0 (**) (* auto fail without -HTU *)
-  lapply (cpds_aaa … HT … HTU) -HTU #H
+| #a #G #L #V #W #W0 #T #U #l #_ #_ #Hl #HVW #HW0 #HTU * #B #HV * #X #HT
+  lapply (aaa_cpds_conf h g … HV W0 ?) [ -HTU /3 width=4/ ] -W #HW0 (**) (* auto fail without -HTU *)
+  lapply (aaa_cpds_conf … HT … HTU) -HTU #H
   elim (aaa_inv_abst … H) -H #B0 #A #H1 #HU #H2 destruct
   lapply (aaa_mono … H1 … HW0) -W0 #H destruct /3 width=4/
-| #G #L #W #T #U #l #_ #_ #HTU #HUW * #B #HW * #A #HT
-  lapply (aaa_cpcs_mono … HUW A … HW) -HUW /2 width=7/ -HTU #H destruct /3 width=3/
+| #G #L #W #T #U #l #_ #_ #_ #HTU #HUW * #B #HW * #A #HT
+  lapply (aaa_ssta_conf … HT … HTU) -HTU #H
+  lapply (aaa_cpcs_mono … HUW … H … HW) -HUW -H #H destruct /3 width=3/
 ]
 qed-.
 
 lemma snv_fwd_csn: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] → ⦃G, L⦄ ⊢ ⬊*[h, g] T.
 #h #g #G #L #T #H elim (snv_fwd_aaa … H) -H /2 width=2/
 qed-.
+
+(* Advanced forward lemmas **************************************************)
+
+lemma snv_fwd_da: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] → ∃l. ⦃G, L⦄ ⊢ T ▪[h, g] l.
+#h #g #G #L #T #H elim (snv_fwd_aaa … H) -H /2 width=2 by aaa_fwd_da/
+qed-.
+
+lemma snv_fwd_ssta: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] → ∃U. ⦃G, L⦄ ⊢ T •[h, g] U.
+#h #g #G #L #T #H elim (snv_fwd_aaa … H) -H /2 width=2 by aaa_fwd_ssta/
+qed-.
+
+lemma snv_lsstas_fwd_correct: ∀h,g,G,L,T1,T2,l. ⦃G, L⦄ ⊢ T1 ¡[h, g] → ⦃G, L⦄ ⊢ T1 •* [h, g, l] T2 →
+                              ∃U2. ⦃G, L⦄ ⊢ T2 •[h, g] U2.
+#h #g #G #L #T1 #T2 #l #HT1 #HT12
+elim (snv_fwd_ssta … HT1) -HT1 /2 width=5 by lsstas_fwd_correct/
+qed-.
+
+(* Advanced properties ******************************************************)
+
+lemma snv_scast: ∀h,g,G,L,V,W,l. ⦃G, L⦄ ⊢ V ¡[h, g] → ⦃G, L⦄ ⊢ W ¡[h, g] →
+                 scast h g l G L V W → ⦃G, L⦄ ⊢V ▪[h, g] l+1 → ⦃G, L⦄ ⊢ ⓝW.V ¡[h, g].
+#h #g #G #L #V #W #l #HV #HW #H #Hl
+elim (snv_fwd_ssta … HV) /4 width=6 by snv_cast, ssta_lsstas/
+qed-.