initial definition of λδ model

[helm.git] / matita / matita / contribs / lambdadelta / apps_2 / models / deq.ma

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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "apps_2/notation/models/ringeq_4.ma".
+include "apps_2/models/model_li.ma".
+include "apps_2/models/model_props.ma".
+
+(* DENOTATIONAL EQUIVALENCE  ************************************************)
+
+definition deq (M): relation3 lenv term term ≝
+                    λL,T1,T2. ∀gv,lv. lv ϵ ⟦L⟧[gv] → ⟦T1⟧[gv, lv] ≗{M} ⟦T2⟧[gv, lv].
+
+interpretation "denotational equivalence (model)"
+   'RingEq M L T1 T2 = (deq M L T1 T2).
+
+(* Basic properties *********************************************************)
+
+lemma deq_refl (M): is_model M →
+                    c_reflexive … (deq M).
+/2 width=1 by mq/ qed.
+(*
+lemma veq_sym: ∀M. symmetric … (veq M).
+// qed-.
+
+theorem veq_trans: ∀M. transitive … (veq M).
+// qed-.
+*)