--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||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/models/model_push.ma".
+
+(* MODEL ********************************************************************)
+
+record is_model (M): Prop ≝ {
+ mq: reflexive … (sq M);
+ ms: ∀gv,lv,s. ⟦⋆s⟧{M}[gv, lv] ≗ sv M s;
+ ml: ∀gv,lv,i. ⟦#i⟧{M}[gv, lv] ≗ lv i;
+ mg: ∀gv,lv,l. ⟦§l⟧{M}[gv, lv] ≗ gv l;
+ md: ∀gv,lv,p,V,T. ⟦ⓓ{p}V.T⟧{M}[gv, lv] ≗ ⟦T⟧[gv, ⫯[⟦V⟧[gv, lv]]lv];
+ mi: ∀gv,lv1,lv2,p,W,T. ⟦W⟧{M}[gv, lv1] ≗ ⟦W⟧{M}[gv, lv2] →
+ (∀d. ⟦T⟧{M}[gv, ⫯[d]lv1] ≗ ⟦T⟧{M}[gv, ⫯[d]lv2]) →
+ ⟦ⓛ{p}W.T⟧[gv, lv1] ≗ ⟦ⓛ{p}W.T⟧[gv, lv2];
+ ma: ∀gv,lv,V,T. ⟦ⓐV.T⟧{M}[gv, lv] ≗ ⟦V⟧[gv, lv] @ ⟦T⟧[gv, lv];
+ me: ∀gv,lv,W,T. ⟦ⓝW.T⟧{M}[gv, lv] ≗ ⟦T⟧[gv, lv];
+ mb: ∀gv,lv,d,p,W,T. d @ ⟦ⓛ{p}W.T⟧{M}[gv, lv] ≗ ⟦T⟧[gv, ⫯[d]lv]
+}.
+
+record is_extensional (M): Prop ≝ {
+ mx: ∀gv,lv1,lv2,p,W1,W2,T1,T2. ⟦W1⟧{M}[gv, lv1] ≗ ⟦W2⟧{M}[gv, lv2] →
+ (∀d. ⟦T1⟧{M}[gv, ⫯[d]lv1] ≗ ⟦T2⟧{M}[gv, ⫯[d]lv2]) →
+ ⟦ⓛ{p}W1.T1⟧[gv, lv1] ≗ ⟦ⓛ{p}W2.T2⟧[gv, lv2]
+}.