--- /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 *)
+(* *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(* Progetto FreeScale *)
+(* *)
+(* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppo: 2008-2010 *)
+(* *)
+(* ********************************************************************** *)
+
+include "emulator/opcodes/Freescale_pseudo_lemmas.ma".
+include "emulator/opcodes/Freescale_instr_mode_lemmas.ma".
+include "emulator/opcodes/IP2022_pseudo_lemmas.ma".
+include "emulator/opcodes/IP2022_instr_mode_lemmas.ma".
+include "emulator/opcodes/pseudo.ma".
+
+nlemma eq_to_eqpseudo : ∀m.∀n1,n2.(n1 = n2) → (eq_pseudo m n1 n2 = true).
+ #m; nelim m;
+ ##[ ##1,2,3,4: napply eq_to_eqFreescalepseudo
+ ##| ##5: napply eq_to_eqIP2022pseudo
+ ##]
+nqed.
+
+nlemma neqpseudo_to_neq : ∀m.∀n1,n2.(eq_pseudo m n1 n2 = false) → (n1 ≠ n2).
+ #m; nelim m;
+ ##[ ##1,2,3,4: napply neqFreescalepseudo_to_neq
+ ##| ##5: napply neqIP2022pseudo_to_neq
+ ##]
+nqed.
+
+nlemma eqpseudo_to_eq : ∀m.∀n1,n2.(eq_pseudo m n1 n2 = true) → (n1 = n2).
+ #m; nelim m;
+ ##[ ##1,2,3,4: napply eqFreescalepseudo_to_eq
+ ##| ##5: napply eqIP2022pseudo_to_eq
+ ##]
+nqed.
+
+nlemma neq_to_neqpseudo : ∀m.∀n1,n2.(n1 ≠ n2) → (eq_pseudo m n1 n2 = false).
+ #m; nelim m;
+ ##[ ##1,2,3,4: napply neq_to_neqFreescalepseudo
+ ##| ##5: napply neq_to_neqIP2022pseudo
+ ##]
+nqed.
+
+nlemma decidable_pseudo : ∀m.∀x,y:aux_pseudo_type m.decidable (x = y).
+ #m; nelim m;
+ ##[ ##1,2,3,4: napply decidable_Freescalepseudo
+ ##| ##5: napply decidable_IP2022pseudo
+ ##]
+nqed.
+
+nlemma symmetric_eqpseudo : ∀m.symmetricT (aux_pseudo_type m) bool (eq_pseudo m).
+ #m; nelim m;
+ ##[ ##1,2,3,4: napply symmetric_eqFreescalepseudo
+ ##| ##5: napply symmetric_eqIP2022pseudo
+ ##]
+nqed.
+
+nlemma eq_to_eqim : ∀m.∀n1,n2.(n1 = n2) → (eq_im m n1 n2 = true).
+ #m; nelim m;
+ ##[ ##1,2,3,4: napply eq_to_eqFreescaleim
+ ##| ##5: napply eq_to_eqIP2022im
+ ##]
+nqed.
+
+nlemma neqim_to_neq : ∀m.∀n1,n2.(eq_im m n1 n2 = false) → (n1 ≠ n2).
+ #m; nelim m;
+ ##[ ##1,2,3,4: napply neqFreescaleim_to_neq
+ ##| ##5: napply neqIP2022im_to_neq
+ ##]
+nqed.
+
+nlemma eqim_to_eq : ∀m.∀n1,n2.(eq_im m n1 n2 = true) → (n1 = n2).
+ #m; nelim m;
+ ##[ ##1,2,3,4: napply eqFreescaleim_to_eq
+ ##| ##5: napply eqIP2022im_to_eq
+ ##]
+nqed.
+
+nlemma neq_to_neqim : ∀m.∀n1,n2.(n1 ≠ n2) → (eq_im m n1 n2 = false).
+ #m; nelim m;
+ ##[ ##1,2,3,4: napply neq_to_neqFreescaleim
+ ##| ##5: napply neq_to_neqIP2022im
+ ##]
+nqed.
+
+nlemma decidable_im : ∀m.∀x,y:aux_im_type m.decidable (x = y).
+ #m; nelim m;
+ ##[ ##1,2,3,4: napply decidable_Freescaleim
+ ##| ##5: napply decidable_IP2022im
+ ##]
+nqed.
+
+nlemma symmetric_eqim : ∀m.symmetricT (aux_im_type m) bool (eq_im m).
+ #m; nelim m;
+ ##[ ##1,2,3,4: napply symmetric_eqFreescaleim
+ ##| ##5: napply symmetric_eqIP2022im
+ ##]
+nqed.