- we introduce extended existentials (generated)

- we exploit the tactic "*" to reduce the volume of decompositions

diff --git a/matita/matita/lib/lambda-delta/ground.ma b/matita/matita/lib/lambda-delta/ground.ma
index 72a1eaf294443850b6d0ba2b149e21095f4cf797..651c2dd99eeffa3e62032ec6d88a476c4a6d071e 100644 (file)
--- a/matita/matita/lib/lambda-delta/ground.ma
+++ b/matita/matita/lib/lambda-delta/ground.ma
@@ -10,6 +10,8 @@
       V_______________________________________________________________ *)
 
 include "basics/list.ma".
+include "lambda-delta/xoa_defs.ma".
+include "lambda-delta/xoa_notation.ma".
 include "lambda-delta/notation.ma".
 
 (* ARITHMETICAL PROPERTIES **************************************************)

diff --git a/matita/matita/lib/lambda-delta/substitution/lift.ma b/matita/matita/lib/lambda-delta/substitution/lift.ma
index 181642504a8fdcff1c642980c43e26b59f063b94..9067889686fa20b2552600edb32e3de17ffd228a 100644 (file)
--- a/matita/matita/lib/lambda-delta/substitution/lift.ma
+++ b/matita/matita/lib/lambda-delta/substitution/lift.ma
@@ -60,18 +60,20 @@ qed.
 
 lemma lift_inv_con22_aux: ∀d,e,T1,T2. ↑[d,e] T1 ≡ T2 →
                           ∀I,V2,U2. T2 = ♭I V2.U2 →
-                          ∃V1,U1. ↑[d,e] V1 ≡ V2 ∧ ↑[d+1,e] U1 ≡ U2 ∧
-                                  T1 = ♭I V1.U1.
+                          ∃∃V1,U1. ↑[d,e] V1 ≡ V2 & ↑[d+1,e] U1 ≡ U2 &
+                                   T1 = ♭I V1.U1.
 #d #e #T1 #T2 #H elim H -H d e T1 T2
    [ #k #d #e #I #V2 #U2 #H destruct
    | #i #d #e #_ #I #V2 #U2 #H destruct
    | #i #d #e #_ #I #V2 #U2 #H destruct
-   | #J #W1 #W2 #T1 #T2 #d #e #HW #HT #_ #_ #I #V2 #U2 #H destruct /5/
+   | #J #W1 #W2 #T1 #T2 #d #e #HW #HT #_ #_ #I #V2 #U2 #H destruct
+     /2 width = 5/
+   ]
 qed.
 
 lemma lift_inv_con22: ∀d,e,T1,I,V2,U2. ↑[d,e] T1 ≡  ♭I V2. U2 →
-                      ∃V1,U1. ↑[d,e] V1 ≡ V2 ∧ ↑[d+1,e] U1 ≡ U2 ∧
-                              T1 = ♭I V1. U1.
+                      ∃∃V1,U1. ↑[d,e] V1 ≡ V2 & ↑[d+1,e] U1 ≡ U2 &
+                               T1 = ♭I V1. U1.
 #d #e #T1 #I #V2 #U2 #H lapply (lift_inv_con22_aux … H) /2/
 qed.
 
@@ -80,57 +82,44 @@ qed.
 theorem lift_trans_rev: ∀d1,e1,T1,T. ↑[d1,e1] T1 ≡ T →
                         ∀d2,e2,T2. ↑[d2 + e1, e2] T2 ≡ T →
                         d1 ≤ d2 →
-                        ∃T0. ↑[d1, e1] T0 ≡ T2 ∧ ↑[d2, e2] T0 ≡ T1.
+                        ∃∃T0. ↑[d1, e1] T0 ≡ T2 & ↑[d2, e2] T0 ≡ T1.
 #d1 #e1 #T1 #T #H elim H -H d1 e1 T1 T
    [ #k #d1 #e1 #d2 #e2 #T2 #Hk #Hd12
      lapply (lift_inv_sort2 … Hk) -Hk #Hk destruct -T2 /3/
    | #i #d1 #e1 #Hid1 #d2 #e2 #T2 #Hi #Hd12
-     lapply (lift_inv_lref2 … Hi) -Hi #H
-     elim H -H #H elim H -H #Hid2 #Hi (**) (* decompose*)
-     destruct -T2
-     [ -Hid2 /5/ (**) (* /4/ *)
+     lapply (lift_inv_lref2 … Hi) -Hi * * #Hid2 #H destruct -T2
+     [ -Hid2 /4/
      | elim (lt_false d1 ?)
        @(le_to_lt_to_lt … Hd12) -Hd12 @(le_to_lt_to_lt … Hid1) -Hid1 /2/
      ]
    | #i #d1 #e1 #Hid1 #d2 #e2 #T2 #Hi #Hd12
-     lapply (lift_inv_lref2 … Hi) -Hi #H
-     elim H -H #H elim H -H #Hid2 #Hi (**) (* decompose*)
-     destruct -T2
-     [ -Hd12; lapply (lt_plus_to_lt_l … Hid2) -Hid2 #Hid2 /4/
+     lapply (lift_inv_lref2 … Hi) -Hi * * #Hid2 #H destruct -T2
+     [ -Hd12; lapply (lt_plus_to_lt_l … Hid2) -Hid2 #Hid2 /3/
      | -Hid1; lapply (arith1 … Hid2) -Hid2 #Hid2
-       @(ex_intro … #(i - e2)) @conj
+       @(ex2_1_intro … #(i - e2))
        [ >le_plus_minus_comm [ @lift_lref_ge @(transitive_le … Hd12) -Hd12 /2/ | -Hd12 /2/ ]
        | -Hd12 >(plus_minus_m_m i e2) in ⊢ (? ? ? ? %) /3/
        ]
      ]
    | #I #W1 #W #U1 #U #d1 #e1 #_ #_ #IHW #IHU #d2 #e2 #T2 #H #Hd12
-     lapply (lift_inv_con22 … H) -H #H
-     elim H -H #W2 #H elim H -H #U2 #H elim H -H #H elim H -H #HW2 #HU2 #H (**) (* decompose*)
-     destruct -T2;
-     elim (IHW … HW2 ?) // -IHW HW2 #W0 #H
-     elim H -H #HW2 #HW1 (**) (* decompose*)
-     >plus_plus_comm_23 in HU2 #HU2 elim (IHU … HU2 ?) /2/ -IHU HU2 Hd12 #U0 #H
-     elim H -H #HU2 #HU1 (**) (* decompose*)
-     @(ex_intro … ♭I W0. U0) /3/ (**) (* /4/ *)
+     lapply (lift_inv_con22 … H) -H * #W2 #U2 #HW2 #HU2 #H destruct -T2;
+     elim (IHW … HW2 ?) // -IHW HW2 #W0 #HW2 #HW1
+     >plus_plus_comm_23 in HU2 #HU2 elim (IHU … HU2 ?) /3 width = 5/
    ]
 qed.
 
 theorem lift_free: ∀d1,e2,T1,T2. ↑[d1, e2] T1 ≡ T2 → ∀d2,e1.
                                  d1 ≤ d2 → d2 ≤ d1 + e1 → e1 ≤ e2 →
-                                 ∃T. ↑[d1, e1] T1 ≡ T ∧ ↑[d2, e2 - e1] T ≡ T2.
+                                 ∃∃T. ↑[d1, e1] T1 ≡ T & ↑[d2, e2 - e1] T ≡ T2.
 #d1 #e2 #T1 #T2 #H elim H -H d1 e2 T1 T2
    [ /3/
    | #i #d1 #e2 #Hid1 #d2 #e1 #Hd12 #_ #_
      lapply (lt_to_le_to_lt … Hid1 Hd12) -Hd12 #Hid2 /4/
    | #i #d1 #e2 #Hid1 #d2 #e1 #_ #Hd21 #He12
      lapply (transitive_le …(i+e1) Hd21 ?) /2/ -Hd21 #Hd21
-     <(plus_plus_minus_m_m e1 e2 i) //
-     @(ex_intro … #(i+e1)) /3/ (**) (* /4/ *)
+     <(plus_plus_minus_m_m e1 e2 i) /3/
    | #I #V1 #V2 #T1 #T2 #d1 #e2 #_ #_ #IHV #IHT #d2 #e1 #Hd12 #Hd21 #He12
-     elim (IHV … Hd12 Hd21 He12) -IHV #V0 #H
-     elim H -H #HV0a #HV0b (**) (* decompose *)
-     elim (IHT (d2+1) … ? ? He12) /2/ -IHT Hd12 Hd21 He12 #T0 #H
-     elim H -H #HT0a #HT0b (**) (* decompose *)
-     @(ex_intro … ♭I V0.T0) /3/ (**) (* /4/ *)
+     elim (IHV … Hd12 Hd21 He12) -IHV #V0 #HV0a #HV0b 
+     elim (IHT (d2+1) … ? ? He12) /3 width = 5/
    ]
 qed.

diff --git a/matita/matita/lib/lambda-delta/substitution/thin.ma b/matita/matita/lib/lambda-delta/substitution/thin.ma
index 00e52947de0b7fef67eaddd4e8d7b6772fd3fbe5..ab1c5f2717e472a25108c32dc7abc987c9fdd83c 100644 (file)
--- a/matita/matita/lib/lambda-delta/substitution/thin.ma
+++ b/matita/matita/lib/lambda-delta/substitution/thin.ma
@@ -32,4 +32,4 @@ axiom thin_conf_ge: ∀d1,e1,L,L1. ↓[d1,e1] L ≡ L1 →
 axiom thin_conf_lt: ∀d1,e1,L,L1. ↓[d1,e1] L ≡ L1 →
                     ∀e2,K2,I,V2. ↓[0,e2] L ≡ K2. ♭I V2 →
                     e2 < d1 → let d ≝ d1 - e2 - 1 in
-                    ∃K1,V1. ↓[0,e2] L1 ≡ K1. ♭I V1 ∧ ↓[d,e1] K2 ≡ K1 ∧ ↑[d,e1] V1 ≡ V2.
+                    ∃∃K1,V1. ↓[0,e2] L1 ≡ K1. ♭I V1 & ↓[d,e1] K2 ≡ K1 & ↑[d,e1] V1 ≡ V2.

diff --git a/matita/matita/lib/lambda-delta/xoa_defs.ma b/matita/matita/lib/lambda-delta/xoa_defs.ma
new file mode 100644 (file)
index 0000000..e36373e
--- /dev/null
+++ b/matita/matita/lib/lambda-delta/xoa_defs.ma
@@ -0,0 +1,30 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* This file was generated by xoa.native: do not edit *********************)
+
+include "basics/pts.ma".
+
+inductive ex2_1 (A0:Type[0]) (P0,P1:A0→Prop) : Prop ≝
+   | ex2_1_intro: ∀x0. (P0 x0)→(P1 x0)→(ex2_1 ? ? ?)
+.
+
+interpretation "multiple existental quantifier (2, 1)" 'Ex P0 P1 = (ex2_1 ? P0 P1).
+
+inductive ex3_2 (A0,A1:Type[0]) (P0,P1,P2:A0→A1→Prop) : Prop ≝
+   | ex3_2_intro: ∀x0,x1. (P0 x0 x1)→(P1 x0 x1)→(P2 x0 x1)→(ex3_2 ? ? ? ? ?)
+.
+
+interpretation "multiple existental quantifier (3, 2)" 'Ex P0 P1 P2 = (ex3_2 ? ? P0 P1 P2).
+

diff --git a/matita/matita/lib/lambda-delta/xoa_notation.ma b/matita/matita/lib/lambda-delta/xoa_notation.ma
new file mode 100644 (file)
index 0000000..1af6c7f
--- /dev/null
+++ b/matita/matita/lib/lambda-delta/xoa_notation.ma
@@ -0,0 +1,24 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* This file was generated by xoa.native: do not edit *********************)
+
+notation "hvbox(∃∃ ident x0 . term 19 P0 & term 19 P1)"
+ non associative with precedence 20
+ for @{ 'Ex (λ${ident x0}.$P0) (λ${ident x0}.$P1) }.
+
+notation "hvbox(∃∃ ident x0 , ident x1 . term 19 P0 & term 19 P1 & term 19 P2)"
+ non associative with precedence 20
+ for @{ 'Ex (λ${ident x0},${ident x1}.$P0) (λ${ident x0},${ident x1}.$P1) (λ${ident x0},${ident x1}.$P2) }.
+