- ng_refiner:

[helm.git] / matita / matita / contribs / lambda / paths / labeled_st_reduction.ma

diff --git a/matita/matita/contribs/lambda/paths/labeled_st_reduction.ma b/matita/matita/contribs/lambda/paths/labeled_st_reduction.ma
index 101954e59a3d3c5d074ab41e7d12505ebb2b63a2..2f93b35afda99911f8c82f7df482c457e1b18e07 100644 (file)
--- a/matita/matita/contribs/lambda/paths/labeled_st_reduction.ma
+++ b/matita/matita/contribs/lambda/paths/labeled_st_reduction.ma
@@ -118,6 +118,21 @@ lemma pl_st_inv_dx: ∀p,F,G. F Ⓡ↦[p] G → ∀q. dx::q = p →
 ]
 qed-.
 
+lemma pl_st_inv_pl_sred: ∀p. in_whd p → ∀M1,F2. {⊤}⇑M1 Ⓡ↦[p] F2 →
+                         ∃∃M2. M1 ↦[p] M2 & {⊤}⇑M2 = F2.
+#p @(in_whd_ind … p) -p
+[ #M1 #F2 #H
+  elim (pl_st_inv_nil … H …) -H // #V #T #HM1 #H
+  elim (boolean_inv_appl … (sym_eq … HM1)) -HM1 #B #N #_ #HB #HN #HM1
+  elim (boolean_inv_abst … HN) -HN #A #_ #HA #HN destruct /2 width=3/
+| #p #_ #IHp #M1 #F2 #H
+  elim (pl_st_inv_dx … H …) -H [3: // |2:skip ] #b #V #T1 #T2 #HT12 #HM1 #H (**) (* simplify line *)
+  elim (boolean_inv_appl … (sym_eq … HM1)) -HM1 #B #A #Hb #HB #HA #HM1 destruct
+  elim (IHp … HT12) -IHp -HT12 #C #HAC #H destruct
+  @(ex2_intro … (@B.C)) // /2 width=1/ (**) (* auto needs some help here *)
+]
+qed-.
+
 lemma pl_st_lift: ∀p. sliftable (pl_st p).
 #p #h #F1 #F2 #H elim H -p -F1 -F2 /2 width=1/
 [ #V #T #d normalize <sdsubst_slift_le //
@@ -155,28 +170,28 @@ lemma pl_st_dsubst: ∀p. sdsubstable_f_dx … (booleanized ⊥) (pl_st p).
 ]
 qed.
 
-lemma pl_st_inv_empty: ∀p,G1,G2. G1 Ⓡ↦[p] G2 → ∀F1. {⊥}⇕F1 = G1 → ⊥.
+lemma pl_st_inv_empty: ∀p,F1,F2. F1 Ⓡ↦[p] F2 → ∀M1. {⊥}⇑M1 = F1 → ⊥.
 #p #F1 #F2 #H elim H -p -F1 -F2
-[ #V #T #F1 #H
-  elim (booleanized_inv_appl … H) -H #c #W #U #H destruct
-| #b #p #T1 #T2 #_ #IHT12 #F1 #H
-  elim (booleanized_inv_abst … H) -H /2 width=2/
-| #b #p #V1 #V2 #T #_ #IHV12 #F1 #H
-  elim (booleanized_inv_appl … H) -H /2 width=2/
-| #b #p #V #T1 #T2 #_ #IHT12 #F1 #H
-  elim (booleanized_inv_appl … H) -H /2 width=2/
+[ #V #T #M1 #H
+  elim (boolean_inv_appl … H) -H #B #A #H destruct
+| #b #p #T1 #T2 #_ #IHT12 #M1 #H
+  elim (boolean_inv_abst … H) -H /2 width=2/
+| #b #p #V1 #V2 #T #_ #IHV12 #M1 #H
+  elim (boolean_inv_appl … H) -H /2 width=2/
+| #b #p #V #T1 #T2 #_ #IHT12 #M1 #H
+  elim (boolean_inv_appl … H) -H /2 width=2/
 ]
 qed-.
 
 theorem pl_st_mono: ∀p. singlevalued … (pl_st p).
 #p #F #G1 #H elim H -p -F -G1
-[ #V #T #G2 #H elim (pl_st_inv_nil … H ?) -H //
+[ #V #T #G2 #H elim (pl_st_inv_nil … H …) -H //
   #W #U #H #HG2 destruct //
-| #b #p #T1 #T2 #_ #IHT12 #G2 #H elim (pl_st_inv_rc … H ??) -H [3: // |2: skip ] (**) (* simplify line *)
+| #b #p #T1 #T2 #_ #IHT12 #G2 #H elim (pl_st_inv_rc … H …) -H [3: // |2: skip ] (**) (* simplify line *)
   #c #U1 #U2 #HU12 #H #HG2 destruct /3 width=1/
-| #b #p #V1 #V2 #T #_ #IHV12 #G2 #H elim (pl_st_inv_sn … H ??) -H [3: // |2: skip ] (**) (* simplify line *)
+| #b #p #V1 #V2 #T #_ #IHV12 #G2 #H elim (pl_st_inv_sn … H …) -H [3: // |2: skip ] (**) (* simplify line *)
   #c #W1 #W2 #U #HW12 #H #HG2 destruct /3 width=1/
-| #b #p #V #T1 #T2 #_ #IHT12 #G2 #H elim (pl_st_inv_dx … H ??) -H [3: // |2: skip ] (**) (* simplify line *)
+| #b #p #V #T1 #T2 #_ #IHT12 #G2 #H elim (pl_st_inv_dx … H …) -H [3: // |2: skip ] (**) (* simplify line *)
   #c #W #U1 #U2 #HU12 #H #HG2 destruct /3 width=1/
 ]
 qed-.
@@ -184,14 +199,14 @@ qed-.
 theorem pl_st_fwd_sle: ∀p1,F1,F. F1 Ⓡ↦[p1] F →
                        ∀p2,F2. F Ⓡ↦[p2] F2 → p1 ≤ p2.
 #p1 #F1 #F #H elim H -p1 -F1 -F //
-[ #b #p #T1 #T #_ #IHT1 #p2 #F2 #H elim (pl_st_inv_abst … H ???) -H [3: // |2,4: skip ] (**) (* simplify line *)
+[ #b #p #T1 #T #_ #IHT1 #p2 #F2 #H elim (pl_st_inv_abst … H …) -H [3: // |2,4: skip ] (**) (* simplify line *)
   #q #T2 #HT2 #H1 #H2 destruct /3 width=2/
-| #b #p #V1 #V #T #_ #IHV1 #p2 #F2 #H elim (pl_st_inv_appl … H ????) -H [7: // |2,3,4: skip ] * (**) (* simplify line *)
+| #b #p #V1 #V #T #_ #IHV1 #p2 #F2 #H elim (pl_st_inv_appl … H …) -H [7: // |2,3,4: skip ] * (**) (* simplify line *)
   [ #U #H destruct
   | #q #V2 #H1 #HV2 #H2 destruct /3 width=2/
-  | #q #U #_ #H elim (pl_st_inv_empty … H ??) [ // | skip ] (**) (* simplify line *)
+  | #q #U #_ #H elim (pl_st_inv_empty … H …) [ // | skip ] (**) (* simplify line *)
   ]
-| #b #p #V #T1 #T #HT1 #IHT1 #p2 #F2 #H elim (pl_st_inv_appl … H ????) -H [7: // |2,3,4: skip ] * (**) (* simplify line *)
+| #b #p #V #T1 #T #HT1 #IHT1 #p2 #F2 #H elim (pl_st_inv_appl … H …) -H [7: // |2,3,4: skip ] * (**) (* simplify line *)
   [ #U #_ #H1 #H2 #_ -b -V -F2 -IHT1
     elim (pl_st_fwd_abst … HT1 … H2) // -H1 * #q #H
     elim (pl_st_inv_rc … HT1 … H) -HT1 -H #b #U1 #U2 #_ #_ #H -b -q -T1 -U1 destruct