- lambdadelta: more service lemmas ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / reducibility / fpr_cpr.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reducibility/fpr_cpr.ma b/matita/matita/contribs/lambdadelta/basic_2/reducibility/fpr_cpr.ma
index 0de0b98f58d8c9b622b6286e6596718fe10a886a..9bd19002a5a6afed1709e7e8f3e91e46d016b0d0 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reducibility/fpr_cpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reducibility/fpr_cpr.ma
@@ -21,7 +21,7 @@ include "basic_2/reducibility/cfpr_cpr.ma".
 lemma cpr_fpr: ∀L,T1,T2. L ⊢ T1 ➡ T2 → ⦃L, T1⦄ ➡ ⦃L, T2⦄.
 /2 width=4/ qed.
 
-(* Advanced propertis *******************************************************)
+(* Advanced properties ******************************************************)
 
 lemma fpr_bind_sn: ∀L1,L2,V1,V2. ⦃L1, V1⦄ ➡ ⦃L2, V2⦄ → ∀T1,T2. T1 ➡ T2 →
                    ∀a,I. ⦃L1, ⓑ{a,I}V1.T1⦄ ➡ ⦃L2, ⓑ{a,I}V2.T2⦄.
@@ -31,6 +31,14 @@ qed.
 
 (* Advanced forward lemmas **************************************************)
 
+lemma fpr_fwd_bind2_minus: ∀I,L1,L,V1,T1,T. ⦃L1, -ⓑ{I}V1.T1⦄ ➡ ⦃L, T⦄ → ∀b.
+                           ∃∃V2,T2. ⦃L1, ⓑ{b,I}V1.T1⦄ ➡ ⦃L, ⓑ{b,I}V2.T2⦄ &
+                                    T = -ⓑ{I}V2.T2.
+#I #L1 #L #V1 #T1 #T #H1 #b
+elim (fpr_inv_all … H1) -H1 #L0 #HL10 #HT1 #HL0
+elim (cpr_fwd_bind1_minus … HT1 b) -HT1 /3 width=4/
+qed-.
+
 lemma fpr_fwd_shift_bind_minus: ∀I1,I2,L1,L2,V1,V2,T1,T2.
                                 ⦃L1, -ⓑ{I1}V1.T1⦄ ➡ ⦃L2, -ⓑ{I2}V2.T2⦄ →
                                 ⦃L1, V1⦄ ➡ ⦃L2, V2⦄ ∧ I1 = I2.
@@ -49,7 +57,7 @@ qed-.
 
 lemma fpr_inv_pair1: ∀I,K1,L2,V1,T1,T2. ⦃K1.ⓑ{I}V1, T1⦄ ➡ ⦃L2, T2⦄ →
                      ∃∃K2,V2. ⦃K1, V1⦄  ➡ ⦃K2, V2⦄ &
-                              ⦃K1, -ⓑ{I}V1.T1⦄ ➡ ⦃K2, -ⓑ{I}V2.T2⦄  &
+                              ⦃K1, -ⓑ{I}V1.T1⦄ ➡ ⦃K2, -ⓑ{I}V2.T2⦄ &
                               L2 = K2.ⓑ{I}V2.
 #I1 #K1 #X #V1 #T1 #T2 #H
 elim (fpr_fwd_pair1 … H) -H #I2 #K2 #V2 #HT12 #H destruct
@@ -58,9 +66,20 @@ qed-.
 
 lemma fpr_inv_pair3: ∀I,L1,K2,V2,T1,T2. ⦃L1, T1⦄ ➡ ⦃K2.ⓑ{I}V2, T2⦄ →
                      ∃∃K1,V1. ⦃K1, V1⦄  ➡ ⦃K2, V2⦄ &
-                              ⦃K1, -ⓑ{I}V1.T1⦄ ➡ ⦃K2, -ⓑ{I}V2.T2⦄  &
+                              ⦃K1, -ⓑ{I}V1.T1⦄ ➡ ⦃K2, -ⓑ{I}V2.T2⦄ &
                               L1 = K1.ⓑ{I}V1.
 #I2 #X #K2 #V2 #T1 #T2 #H
 elim (fpr_fwd_pair3 … H) -H #I1 #K1 #V1 #HT12 #H destruct
 elim (fpr_fwd_shift_bind_minus … HT12) #HV12 #H destruct /2 width=5/
 qed-.
+
+(* More advanced forward lemmas *********************************************)
+
+lemma fpr_fwd_pair1_full: ∀I,K1,L2,V1,T1,T2. ⦃K1.ⓑ{I}V1, T1⦄ ➡ ⦃L2, T2⦄ →
+                          ∀b. ∃∃K2,V2. ⦃K1, V1⦄  ➡ ⦃K2, V2⦄ &
+                                       ⦃K1, ⓑ{b,I}V1.T1⦄ ➡ ⦃K2, ⓑ{b,I}V2.T2⦄ &
+                                       L2 = K2.ⓑ{I}V2.
+#I #K1 #L2 #V1 #T1 #T2 #H #b
+elim (fpr_inv_pair1 … H) -H #K2 #V2 #HV12 #HT12 #H destruct
+elim (fpr_fwd_bind2_minus … HT12 b) -HT12 #W1 #U1 #HTU1 #H destruct /2 width=5/
+qed-.