--- /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 "num/oct_lemmas.ma".
+include "num/word16_lemmas.ma".
+include "num/word24_lemmas.ma".
+include "emulator/status/IP2022_status.ma".
+include "emulator/memory/memory_struct_lemmas.ma".
+
+(* *********************************** *)
+(* STATUS INTERNO DEL PROCESSORE (ALU) *)
+(* *********************************** *)
+
+nlemma aluIP2022_destruct_1 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x1 = y1.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 a _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ⇒ x1 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_2 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x2 = y2.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ a _ _ _ _ _ _ _ _ _ _ _ _ _ _ ⇒ x2 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_3 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x3 = y3.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ a _ _ _ _ _ _ _ _ _ _ _ _ _ ⇒ x3 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_4 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x4 = y4.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ _ a _ _ _ _ _ _ _ _ _ _ _ _ ⇒ x4 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_5 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x5 = y5.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ _ _ a _ _ _ _ _ _ _ _ _ _ _ ⇒ x5 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_6 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x6 = y6.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ _ _ _ a _ _ _ _ _ _ _ _ _ _ ⇒ x6 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_7 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x7 = y7.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ _ _ _ _ a _ _ _ _ _ _ _ _ _ ⇒ x7 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_8 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x8 = y8.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ _ _ _ _ _ a _ _ _ _ _ _ _ _ ⇒ x8 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_9 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x9 = y9.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ _ _ _ _ _ _ a _ _ _ _ _ _ _ ⇒ x9 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_10 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x10 = y10.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ _ _ _ _ _ _ _ a _ _ _ _ _ _ ⇒ x10 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_11 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x11 = y11.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ _ _ _ _ _ _ _ _ a _ _ _ _ _ ⇒ x11 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_12 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x12 = y12.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ _ _ _ _ _ _ _ _ _ a _ _ _ _ ⇒ x12 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_13 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x13 = y13.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ _ _ _ _ _ _ _ _ _ _ a _ _ _ ⇒ x13 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_14 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x14 = y14.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ _ _ _ _ _ _ _ _ _ _ _ a _ _ ⇒ x14 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_15 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x15 = y15.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ _ _ _ _ _ _ _ _ _ _ _ _ a _ ⇒ x15 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma aluIP2022_destruct_16 :
+∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 =
+ mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 →
+ x16 = y16.
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange with (match mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16
+ with [ mk_alu_IP2022 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ a ⇒ x16 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+naxiom symmetric_eqaluIP2022 : symmetricT alu_IP2022 bool eq_IP2022_alu.
+(* !!! la compilazione avviene ma il tempo e' troppo lungo...
+ #alu1; ncases alu1;
+ #z1; #z2; #z3; #z4; #z5; #z6; #z7; #z8; #z9; #z10; #z11; #z12; #z13; #z14; #z15; #z16;
+ #alu2; ncases alu2;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nchange with (
+ ((eq_b8 z1 y1) ⊗ (eq_b8 z2 y2) ⊗ (eq_b8 z3 y3) ⊗ (eq_ar8 ? eq_w24 z4 y4) ⊗
+ (eq_ar16 ? eq_w16 z5 y5) ⊗ (eq_w16 z6 y6) ⊗ (eq_w16 z7 y7) ⊗ (eq_w16 z8 y8) ⊗
+ (eq_w16 z9 y9) ⊗ (eq_w16 z10 y10) ⊗ (eq_ex z11 y11) ⊗ (eq_oct z12 y12) ⊗
+ (eq_bool z13 y13) ⊗ (eq_bool z14 y14) ⊗ (eq_bool z15 y15) ⊗ (eq_bool z16 y16)) =
+ ((eq_b8 y1 z1) ⊗ (eq_b8 y2 z2) ⊗ (eq_b8 y3 z3) ⊗ (eq_ar8 ? eq_w24 y4 z4) ⊗
+ (eq_ar16 ? eq_w16 y5 z5) ⊗ (eq_w16 y6 z6) ⊗ (eq_w16 y7 z7) ⊗ (eq_w16 y8 z8) ⊗
+ (eq_w16 y9 z9) ⊗ (eq_w16 y10 z10) ⊗ (eq_ex y11 z11) ⊗ (eq_oct y12 z12) ⊗
+ (eq_bool y13 z13) ⊗ (eq_bool y14 z14) ⊗ (eq_bool y15 z15) ⊗ (eq_bool y16 z16)));
+ nrewrite > (symmetric_eqb8 z1 y1);
+ nrewrite > (symmetric_eqb8 z2 y2);
+ nrewrite > (symmetric_eqb8 z3 y3);
+ nrewrite > (symmetric_eqar8 ? eq_w24 symmetric_eqw24 z4 y4);
+ nrewrite > (symmetric_eqar16 ? eq_w16 symmetric_eqw16 z5 y5);
+ nrewrite > (symmetric_eqw16 z6 y6);
+ nrewrite > (symmetric_eqw16 z7 y7);
+ nrewrite > (symmetric_eqw16 z8 y8);
+ nrewrite > (symmetric_eqw16 z9 y9);
+ nrewrite > (symmetric_eqw16 z10 y10);
+ nrewrite > (symmetric_eqex z11 y11);
+ nrewrite > (symmetric_eqoct z12 y12);
+ nrewrite > (symmetric_eqbool z13 y13);
+ nrewrite > (symmetric_eqbool z14 y14);
+ nrewrite > (symmetric_eqbool z15 y15);
+ nrewrite > (symmetric_eqbool z16 y16);
+ napply refl_eq.
+nqed.
+*)
+
+nlemma eqaluIP2022_to_eq : ∀alu1,alu2.eq_IP2022_alu alu1 alu2 = true → alu1 = alu2.
+ #alu1; ncases alu1;
+ #z1; #z2; #z3; #z4; #z5; #z6; #z7; #z8; #z9; #z10; #z11; #z12; #z13; #z14; #z15; #z16;
+ #alu2; ncases alu2;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nchange in H:(%) with (
+ ((eq_b8 z1 y1) ⊗ (eq_b8 z2 y2) ⊗ (eq_b8 z3 y3) ⊗ (eq_ar8 ? eq_w24 z4 y4) ⊗
+ (eq_ar16 ? eq_w16 z5 y5) ⊗ (eq_w16 z6 y6) ⊗ (eq_w16 z7 y7) ⊗ (eq_w16 z8 y8) ⊗
+ (eq_w16 z9 y9) ⊗ (eq_w16 z10 y10) ⊗ (eq_ex z11 y11) ⊗ (eq_oct z12 y12) ⊗
+ (eq_bool z13 y13) ⊗ (eq_bool z14 y14) ⊗ (eq_bool z15 y15) ⊗ (eq_bool z16 y16)) = true);
+ nrewrite > (eqbool_to_eq … (andb_true_true_r … H));
+ nletin H1 ≝ (andb_true_true_l … H);
+ nrewrite > (eqbool_to_eq … (andb_true_true_r … (andb_true_true_l … H)));
+ nletin H2 ≝ (andb_true_true_l … H1);
+ nrewrite > (eqbool_to_eq … (andb_true_true_r … H2));
+ nletin H3 ≝ (andb_true_true_l … H2);
+ nrewrite > (eqbool_to_eq … (andb_true_true_r … H3));
+ nletin H4 ≝ (andb_true_true_l … H3);
+ nrewrite > (eqoct_to_eq … (andb_true_true_r … H4));
+ nletin H5 ≝ (andb_true_true_l … H4);
+ nrewrite > (eqex_to_eq … (andb_true_true_r … H5));
+ nletin H6 ≝ (andb_true_true_l … H5);
+ nrewrite > (eqw16_to_eq … (andb_true_true_r … H6));
+ nletin H7 ≝ (andb_true_true_l … H6);
+ nrewrite > (eqw16_to_eq … (andb_true_true_r … H7));
+ nletin H8 ≝ (andb_true_true_l … H7);
+ nrewrite > (eqw16_to_eq … (andb_true_true_r … H8));
+ nletin H9 ≝ (andb_true_true_l … H8);
+ nrewrite > (eqw16_to_eq … (andb_true_true_r … H9));
+ nletin H10 ≝ (andb_true_true_l … H9);
+ nrewrite > (eqw16_to_eq … (andb_true_true_r … H10));
+ nletin H11 ≝ (andb_true_true_l … H10);
+ nrewrite > (eqar16_to_eq ? eq_w16 eqw16_to_eq … (andb_true_true_r … H11));
+ nletin H12 ≝ (andb_true_true_l … H11);
+ nrewrite > (eqar8_to_eq ? eq_w24 eqw24_to_eq … (andb_true_true_r … H12));
+ nletin H13 ≝ (andb_true_true_l … H12);
+ nrewrite > (eqb8_to_eq … (andb_true_true_r … H13));
+ nletin H14 ≝ (andb_true_true_l … H13);
+ nrewrite > (eqb8_to_eq … (andb_true_true_r … H14));
+ nrewrite > (eqb8_to_eq … (andb_true_true_l … H14));
+ napply refl_eq.
+nqed.
+
+naxiom eq_to_eqaluIP2022 : ∀alu1,alu2.alu1 = alu2 → eq_IP2022_alu alu1 alu2 = true.
+(* !!! la compilazione avviene ma il tempo e' troppo lungo...
+ #alu1; ncases alu1;
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #alu2; ncases alu2;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16; #H;
+ nrewrite > (aluIP2022_destruct_1 … H);
+ nrewrite > (aluIP2022_destruct_2 … H);
+ nrewrite > (aluIP2022_destruct_3 … H);
+ nrewrite > (aluIP2022_destruct_4 … H);
+ nrewrite > (aluIP2022_destruct_5 … H);
+ nrewrite > (aluIP2022_destruct_6 … H);
+ nrewrite > (aluIP2022_destruct_7 … H);
+ nrewrite > (aluIP2022_destruct_8 … H);
+ nrewrite > (aluIP2022_destruct_9 … H);
+ nrewrite > (aluIP2022_destruct_10 … H);
+ nrewrite > (aluIP2022_destruct_11 … H);
+ nrewrite > (aluIP2022_destruct_12 … H);
+ nrewrite > (aluIP2022_destruct_13 … H);
+ nrewrite > (aluIP2022_destruct_14 … H);
+ nrewrite > (aluIP2022_destruct_15 … H);
+ nrewrite > (aluIP2022_destruct_16 … H);
+ nchange with (
+ ((eq_b8 y1 y1) ⊗ (eq_b8 y2 y2) ⊗ (eq_b8 y3 y3) ⊗ (eq_ar8 ? eq_w24 y4 y4) ⊗
+ (eq_ar16 ? eq_w16 y5 y5) ⊗ (eq_w16 y6 y6) ⊗ (eq_w16 y7 y7) ⊗ (eq_w16 y8 y8) ⊗
+ (eq_w16 y9 y9) ⊗ (eq_w16 y10 y10) ⊗ (eq_ex y11 y11) ⊗ (eq_oct y12 y12) ⊗
+ (eq_bool y13 y13) ⊗ (eq_bool y14 y14) ⊗ (eq_bool y15 y15) ⊗ (eq_bool y16 y16)) = true);
+ nrewrite > (eq_to_eqb8 y1 y1 (refl_eq …));
+ nrewrite > (eq_to_eqb8 y2 y2 (refl_eq …));
+ nrewrite > (eq_to_eqb8 y3 y3 (refl_eq …));
+ nrewrite > (eq_to_eqar8 ? eq_w24 eq_to_eqw24 y4 y4 (refl_eq …));
+ nrewrite > (eq_to_eqar16 ? eq_w16 eq_to_eqw16 y5 y5 (refl_eq …));
+ nrewrite > (eq_to_eqw16 y6 y6 (refl_eq …));
+ nrewrite > (eq_to_eqw16 y7 y7 (refl_eq …));
+ nrewrite > (eq_to_eqw16 y8 y8 (refl_eq …));
+ nrewrite > (eq_to_eqw16 y9 y9 (refl_eq …));
+ nrewrite > (eq_to_eqw16 y10 y10 (refl_eq …));
+ nrewrite > (eq_to_ex y11 y11 (refl_eq …));
+ nrewrite > (eq_to_oct y12 y12 (refl_eq …));
+ nrewrite > (eq_to_eqbool y13 y13 (refl_eq …));
+ nrewrite > (eq_to_eqbool y14 y14 (refl_eq …));
+ nrewrite > (eq_to_eqbool y15 y15 (refl_eq …));
+ nrewrite > (eq_to_eqbool y16 y16 (refl_eq …));
+ napply refl_eq.
+nqed.
+*)
+
+nlemma decidable_aluIP2022_aux1
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ (x1 ≠ y1) →
+ (mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (aluIP2022_destruct_1 … H1)).
+nqed.
+
+nlemma decidable_aluIP2022_aux2
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ (x2 ≠ y2) →
+ (mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (aluIP2022_destruct_2 … H1)).
+nqed.
+
+nlemma decidable_aluIP2022_aux3
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ (x3 ≠ y3) →
+ (mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (aluIP2022_destruct_3 … H1)).
+nqed.
+
+nlemma decidable_aluIP2022_aux4
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ (x4 ≠ y4) →
+ (mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (aluIP2022_destruct_4 … H1)).
+nqed.
+
+nlemma decidable_aluIP2022_aux5
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ (x5 ≠ y5) →
+ (mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (aluIP2022_destruct_5 … H1)).
+nqed.
+
+nlemma decidable_aluIP2022_aux6
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ (x6 ≠ y6) →
+ (mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (aluIP2022_destruct_6 … H1)).
+nqed.
+
+nlemma decidable_aluIP2022_aux7
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ (x7 ≠ y7) →
+ (mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (aluIP2022_destruct_7 … H1)).
+nqed.
+
+nlemma decidable_aluIP2022_aux8
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ (x8 ≠ y8) →
+ (mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (aluIP2022_destruct_8 … H1)).
+nqed.
+
+nlemma decidable_aluIP2022_aux9
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ (x9 ≠ y9) →
+ (mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (aluIP2022_destruct_9 … H1)).
+nqed.
+
+nlemma decidable_aluIP2022_aux10
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ (x10 ≠ y10) →
+ (mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (aluIP2022_destruct_10 … H1)).
+nqed.
+
+nlemma decidable_aluIP2022_aux11
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ (x11 ≠ y11) →
+ (mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (aluIP2022_destruct_11 … H1)).
+nqed.
+
+nlemma decidable_aluIP2022_aux12
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ (x12 ≠ y12) →
+ (mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (aluIP2022_destruct_12 … H1)).
+nqed.
+
+nlemma decidable_aluIP2022_aux13
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ (x13 ≠ y13) →
+ (mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (aluIP2022_destruct_13 … H1)).
+nqed.
+
+nlemma decidable_aluIP2022_aux14
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ (x14 ≠ y14) →
+ (mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (aluIP2022_destruct_14 … H1)).
+nqed.
+
+nlemma decidable_aluIP2022_aux15
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ (x15 ≠ y15) →
+ (mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (aluIP2022_destruct_15 … H1)).
+nqed.
+
+nlemma decidable_aluIP2022_aux16
+ : ∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16.
+ (x16 ≠ y16) →
+ (mk_alu_IP2022 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16) ≠
+ (mk_alu_IP2022 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16).
+ #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize; #H; #H1;
+ napply (H (aluIP2022_destruct_16 … H1)).
+nqed.
+
+nlemma decidable_aluIP2022 : ∀x,y:alu_IP2022.decidable (x = y).
+ #x; nelim x; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13; #x14; #x15; #x16;
+ #y; nelim y; #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #y14; #y15; #y16;
+ nnormalize;
+ napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_b8 x1 y1) …);
+ ##[ ##2: #H; napply (or2_intro2 … (decidable_aluIP2022_aux1 … H))
+ ##| ##1: #H; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_b8 x2 y2) …);
+ ##[ ##2: #H1; napply (or2_intro2 … (decidable_aluIP2022_aux2 … H1))
+ ##| ##1: #H1; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_b8 x3 y3) …);
+ ##[ ##2: #H2; napply (or2_intro2 … (decidable_aluIP2022_aux3 … H2))
+ ##| ##1: #H2; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_ar8 ? decidable_w24 x4 y4) …);
+ ##[ ##2: #H3; napply (or2_intro2 … (decidable_aluIP2022_aux4 … H3))
+ ##| ##1: #H3; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_ar16 ? decidable_w16 x5 y5) …);
+ ##[ ##2: #H4; napply (or2_intro2 … (decidable_aluIP2022_aux5 … H4))
+ ##| ##1: #H4; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_w16 x6 y6) …);
+ ##[ ##2: #H5; napply (or2_intro2 … (decidable_aluIP2022_aux6 … H5))
+ ##| ##1: #H5; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_w16 x7 y7) …);
+ ##[ ##2: #H6; napply (or2_intro2 … (decidable_aluIP2022_aux7 … H6))
+ ##| ##1: #H6; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_w16 x8 y8) …);
+ ##[ ##2: #H7; napply (or2_intro2 … (decidable_aluIP2022_aux8 … H7))
+ ##| ##1: #H7; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_w16 x9 y9) …);
+ ##[ ##2: #H8; napply (or2_intro2 … (decidable_aluIP2022_aux9 … H8))
+ ##| ##1: #H8; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_w16 x10 y10) …);
+ ##[ ##2: #H9; napply (or2_intro2 … (decidable_aluIP2022_aux10 … H9))
+ ##| ##1: #H9; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_ex x11 y11) …);
+ ##[ ##2: #H10; napply (or2_intro2 … (decidable_aluIP2022_aux11 … H10))
+ ##| ##1: #H10; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_oct x12 y12) …);
+ ##[ ##2: #H11; napply (or2_intro2 … (decidable_aluIP2022_aux12 … H11))
+ ##| ##1: #H11; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_bool x13 y13) …);
+ ##[ ##2: #H12; napply (or2_intro2 … (decidable_aluIP2022_aux13 … H12))
+ ##| ##1: #H12; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_bool x14 y14) …);
+ ##[ ##2: #H13; napply (or2_intro2 … (decidable_aluIP2022_aux14 … H13))
+ ##| ##1: #H13; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_bool x15 y15) …);
+ ##[ ##2: #H14; napply (or2_intro2 … (decidable_aluIP2022_aux15 … H14))
+ ##| ##1: #H14; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_bool x16 y16) …);
+ ##[ ##2: #H15; napply (or2_intro2 … (decidable_aluIP2022_aux16 … H15))
+ ##| ##1: #H15; nrewrite > H; nrewrite > H1; nrewrite > H2; nrewrite > H3;
+ nrewrite > H4; nrewrite > H5; nrewrite > H6; nrewrite > H7;
+ nrewrite > H8; nrewrite > H9; nrewrite > H10; nrewrite > H11;
+ nrewrite > H12; nrewrite > H13; nrewrite > H14; nrewrite > H15;
+ napply (or2_intro1 (? = ?) (? ≠ ?) (refl_eq …));
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+nqed.
projects / helm.git / blobdiff