update in lambdadelta

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / examples / ex_snv_eta.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/examples/ex_snv_eta.ma b/matita/matita/contribs/lambdadelta/basic_2A/examples/ex_snv_eta.ma
new file mode 100644 (file)
index 0000000..65abf63
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2A/examples/ex_snv_eta.ma
@@ -0,0 +1,61 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2A/dynamic/snv.ma".
+
+(* EXAMPLES *****************************************************************)
+
+(* Extended validy (basic?_2) vs. restricted validity (basic_1) *************)
+
+(* extended validity of a closure, last arg of snv_appl > 1 *)
+lemma snv_extended: ∀h,g,a,G,L,k. ⦃G, L.ⓛ⋆k.ⓛⓛ{a}⋆k.⋆k.ⓛ#0⦄ ⊢ ⓐ#2.#0 ¡[h, g].
+#h #g #a #G #L #k elim (deg_total h g k)
+#d #Hd @(snv_appl … a … (⋆k) … (⋆k) (0+1+1))
+[ /4 width=5 by snv_lref, drop_drop_lt/
+| /4 width=13 by snv_bind, snv_lref/
+| /5 width=6 by lstas_scpds, lstas_succ, da_ldec, da_sort, drop_drop_lt/
+| @(lstas_scpds … (d+1+1))
+  /5 width=11 by lstas_bind, lstas_succ, da_bind, da_ldec, da_sort, lift_bind/
+]
+qed.
+
+(* restricted validity of the η-expanded closure, last arg of snv_appl = 1 **)
+lemma snv_restricted: ∀h,g,a,G,L,k. ⦃G, L.ⓛ⋆k.ⓛⓛ{a}⋆k.⋆k.ⓛⓛ{a}⋆k.ⓐ#0.#1⦄ ⊢ ⓐ#2.#0 ¡[h, g].
+#h #g #a #G #L #k elim (deg_total h g k)
+#d #Hd @(snv_appl … a … (⋆k) … (ⓐ#0.#2) (0+1))
+[ /4 width=5 by snv_lref, drop_drop_lt/
+| @snv_lref [4: // |1,2,3: skip ]
+  @snv_bind //
+  @(snv_appl … a … (⋆k) … (⋆k) (0+1))
+  [ @snv_lref [4: // |1,2,3: skip ] //
+  | @snv_lref [4: /2 width=1 by drop_drop_lt/ |1,2,3: skip ] @snv_bind //
+  | @(lstas_scpds … (d+1)) /3 width=6 by da_sort, da_ldec, lstas_succ/
+  | @(lstas_scpds … (d+1)) /3 width=8 by lstas_succ, lstas_bind, drop_drop, lift_bind/
+    @da_ldec [3: /2 width=1 by drop_drop_lt/ |1,2: skip ] /3 width=1 by da_sort, da_bind/
+  ]
+| /5 width=6 by lstas_scpds, lstas_succ, da_ldec, da_sort, drop_drop_lt/
+| @(lstas_scpds … (d+1+1)) //
+  [ @da_ldec [3: // |1,2: skip ]
+    @da_bind @da_flat @da_ldec [3: /2 width=1 by drop_drop_lt/ |1,2: skip ]
+    /3 width=1 by da_sort, da_bind/
+  | @lstas_succ [4: // |1,2: skip ]
+    [2: @lstas_bind | skip ]
+    [2: @lstas_appl | skip ]
+    [2: @lstas_zero
+        [4: /2 width=1 by drop_drop_lt/ |5: /2 width=2 by lstas_bind/ |*: skip ]
+    |1: skip ]
+    /4 width=2 by lift_flat, lift_bind, lift_lref_ge_minus, lift_lref_lt/
+  ]
+]
+qed.