auxiliary update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm.ma
index a8202b637b7179bfecd06866adf1197fb816a0a9..97cfd31a44e5096dc744e2f55fc528193c7bb303 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm.ma
@@ -119,6 +119,14 @@ qed.
 lemma cpr_refl: ∀h,G,L. reflexive … (cpm h G L 0).
 /3 width=3 by cpg_refl, ex2_intro/ qed.
 
+(* Advanced properties ******************************************************)
+
+lemma cpm_sort (h) (G) (L):
+               ∀n. n ≤ 1 → ∀s. ⦃G,L⦄ ⊢ ⋆s ➡[n,h] ⋆((next h)^n s).
+#h #G #L * //
+#n #H #s <(le_n_O_to_eq n) /2 width=1 by le_S_S_to_le/
+qed.
+
 (* Basic inversion lemmas ***************************************************)
 
 lemma cpm_inv_atom1: ∀n,h,J,G,L,T2. ⦃G, L⦄ ⊢ ⓪{J} ➡[n, h] T2 →
@@ -223,6 +231,13 @@ elim (cpm_inv_bind1 … H) -H
 ]
 qed-.
 
+lemma cpm_inv_abst_bi: ∀n,h,p1,p2,G,L,V1,V2,T1,T2. ⦃G,L⦄ ⊢ ⓛ{p1}V1.T1 ➡[n,h] ⓛ{p2}V2.T2 →
+                       ∧∧ ⦃G,L⦄ ⊢ V1 ➡[h] V2 & ⦃G,L.ⓛV1⦄ ⊢ T1 ➡[n,h] T2 & p1 = p2.
+#n #h #p1 #p2 #G #L #V1 #V2 #T1 #T2 #H
+elim (cpm_inv_abst1 … H) -H #XV #XT #HV #HT #H destruct
+/2 width=1 by and3_intro/  
+qed-.
+
 (* Basic_1: includes: pr0_gen_appl pr2_gen_appl *)
 (* Basic_2A1: includes: cpr_inv_appl1 *)
 lemma cpm_inv_appl1: ∀n,h,G,L,V1,U1,U2. ⦃G, L⦄ ⊢ ⓐ V1.U1 ➡[n, h] U2 →
@@ -275,6 +290,22 @@ lemma cpm_inv_cast1: ∀n,h,G,L,V1,U1,U2. ⦃G, L⦄ ⊢ ⓝV1.U1 ➡[n, h] U2 
 ]
 qed-.
 
+(* Advanced inversion lemmas ************************************************)
+
+lemma cpm_inv_appl_sn_decompose (h) (n) (G) (L) (V1) (T1):
+      ∀X2. ⦃G,L⦄ ⊢ ⓐV1.T1 ➡[n,h] X2 →
+      ∃∃T2. ⦃G,L⦄ ⊢ T1 ➡[n,h] T2 & ⦃G,L⦄ ⊢ ⓐV1.T2 ➡[h] X2.
+#h #n #G #L #V1 #T1 #X2 #H
+elim (cpm_inv_appl1 … H) -H *
+[ #V2 #T2 #HV12 #HT12 #H destruct
+  /3 width=3 by cpm_appl, ex2_intro/
+| #p #V2 #W1 #W2 #U1 #U2 #HV12 #HW12 #HU12 #H1 #H2 destruct
+  /3 width=5 by cpm_beta, cpm_bind, ex2_intro/
+| #p #V2 #V0 #W1 #W2 #U1 #U2 #HV12 #HV20 #HW12 #HU12 #H1 #H2 destruct
+  /3 width=5 by cpm_theta, cpm_bind, ex2_intro/
+]
+qed-.
+
 (* Basic forward lemmas *****************************************************)
 
 (* Basic_2A1: includes: cpr_fwd_bind1_minus *)