update in basic_2 and static_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / cpm_aaa.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm_aaa.ma
index eff341b1d95a0342a7d253a657f0819ef94d89a4..8fa425fc5faec08abbd400c59ac655a22fd0f436 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm_aaa.ma
@@ -22,3 +22,28 @@ include "basic_2/rt_transition/lpx_aaa.ma".
 (* Basic_2A1: includes: cpr_aaa_conf *)
 lemma cpm_aaa_conf (n) (h): ∀G,L. Conf3 … (aaa G L) (cpm h G L n).
 /3 width=5 by cpx_aaa_conf, cpm_fwd_cpx/ qed-.
+
+(* Note: one of these U is the inferred type of T *)
+lemma aaa_cpm_SO (h) (G) (L) (A):
+      ∀T. ⦃G, L⦄ ⊢ T ⁝ A → ∃U. ⦃G,L⦄ ⊢ T ➡[1,h] U.
+#h #G #L #A #T #H elim H -G -L -T -A
+[ /3 width=2 by ex_intro/
+| * #G #L #V #B #_ * #V0 #HV0
+  [ elim (lifts_total V0 (𝐔❴1❵)) #W0 #HVW0
+    /3 width=4 by cpm_delta, ex_intro/
+  | elim (lifts_total V (𝐔❴1❵)) #W #HVW -V0
+    /3 width=4 by cpm_ell, ex_intro/
+  ]
+| #I #G #L #A #i #_ * #T0 #HT0
+  elim (lifts_total T0 (𝐔❴1❵)) #U0 #HTU0
+  /3 width=4 by cpm_lref, ex_intro/
+| #p #G #L #V #T #B #A #_ #_ #_ * #T0 #HT0
+  /3 width=2 by cpm_bind, ex_intro/
+| #p #G #L #V #T #B #A #_ #_ #_  * #T0 #HT0
+  /3 width=2 by cpm_bind, ex_intro/
+| #G #L #V #T #B #A #_ #_ #_ * #T0 #HT0
+  /3 width=2 by cpm_appl, ex_intro/
+| #G #L #U #T #A #_ #_ * #U0 #HU0 * #T0 #HT0
+  /3 width=2 by cpm_cast, ex_intro/
+]
+qed-.