+++ /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: Cosimo Oliboni, oliboni@cs.unibo.it *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
-(* *)
-(* ********************************************************************** *)
-
-include "freescale/word16_lemmas.ma".
-include "freescale/opcode_base_lemmas1.ma".
-include "freescale/status.ma".
-include "freescale/option_lemmas.ma".
-include "freescale/prod_lemmas.ma".
-
-(* *********************************** *)
-(* STATUS INTERNO DEL PROCESSORE (ALU) *)
-(* *********************************** *)
-
-nlemma aluHC05_destruct_1 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
- mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 = mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 →
- x1 = y1.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
- nchange with (match mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13
- with [ mk_alu_HC05 a _ _ _ _ _ _ _ _ _ _ _ _ ⇒ x1 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluHC05_destruct_2 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
- mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 = mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 →
- x2 = y2.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
- nchange with (match mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13
- with [ mk_alu_HC05 _ a _ _ _ _ _ _ _ _ _ _ _ ⇒ x2 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluHC05_destruct_3 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
- mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 = mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 →
- x3 = y3.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
- nchange with (match mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13
- with [ mk_alu_HC05 _ _ a _ _ _ _ _ _ _ _ _ _ ⇒ x3 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluHC05_destruct_4 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
- mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 = mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 →
- x4 = y4.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
- nchange with (match mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13
- with [ mk_alu_HC05 _ _ _ a _ _ _ _ _ _ _ _ _ ⇒ x4 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluHC05_destruct_5 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
- mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 = mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 →
- x5 = y5.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
- nchange with (match mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13
- with [ mk_alu_HC05 _ _ _ _ a _ _ _ _ _ _ _ _ ⇒ x5 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluHC05_destruct_6 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
- mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 = mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 →
- x6 = y6.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
- nchange with (match mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13
- with [ mk_alu_HC05 _ _ _ _ _ a _ _ _ _ _ _ _ ⇒ x6 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluHC05_destruct_7 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
- mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 = mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 →
- x7 = y7.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
- nchange with (match mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13
- with [ mk_alu_HC05 _ _ _ _ _ _ a _ _ _ _ _ _ ⇒ x7 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluHC05_destruct_8 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
- mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 = mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 →
- x8 = y8.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
- nchange with (match mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13
- with [ mk_alu_HC05 _ _ _ _ _ _ _ a _ _ _ _ _ ⇒ x8 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluHC05_destruct_9 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
- mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 = mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 →
- x9 = y9.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
- nchange with (match mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13
- with [ mk_alu_HC05 _ _ _ _ _ _ _ _ a _ _ _ _ ⇒ x9 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluHC05_destruct_10 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
- mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 = mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 →
- x10 = y10.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
- nchange with (match mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13
- with [ mk_alu_HC05 _ _ _ _ _ _ _ _ _ a _ _ _ ⇒ x10 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluHC05_destruct_11 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
- mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 = mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 →
- x11 = y11.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
- nchange with (match mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13
- with [ mk_alu_HC05 _ _ _ _ _ _ _ _ _ _ a _ _ ⇒ x11 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluHC05_destruct_12 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
- mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 = mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 →
- x12 = y12.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
- nchange with (match mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13
- with [ mk_alu_HC05 _ _ _ _ _ _ _ _ _ _ _ a _ ⇒ x12 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluHC05_destruct_13 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13.
- mk_alu_HC05 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 = mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 →
- x13 = y13.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
- nchange with (match mk_alu_HC05 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13
- with [ mk_alu_HC05 _ _ _ _ _ _ _ _ _ _ _ _ a ⇒ x13 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma symmetric_eqaluHC05 : symmetricT alu_HC05 bool eq_alu_HC05.
- #alu1; #alu2;
- ncases alu1;
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
- ncases alu2;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13;
- nchange with (
- ((eq_b8 x1 y1) ⊗ (eq_b8 x2 y2) ⊗ (eq_w16 x3 y3) ⊗ (eq_w16 x4 y4) ⊗
- (eq_w16 x5 y5) ⊗ (eq_w16 x6 y6) ⊗ (eq_w16 x7 y7) ⊗ (eq_bool x8 y8) ⊗
- (eq_bool x9 y9) ⊗ (eq_bool x10 y10) ⊗ (eq_bool x11 y11) ⊗ (eq_bool x12 y12) ⊗
- (eq_bool x13 y13)) = ((eq_b8 y1 x1) ⊗ (eq_b8 y2 x2) ⊗ (eq_w16 y3 x3) ⊗
- (eq_w16 y4 x4) ⊗ (eq_w16 y5 x5) ⊗ (eq_w16 y6 x6) ⊗ (eq_w16 y7 x7) ⊗
- (eq_bool y8 x8) ⊗ (eq_bool y9 x9) ⊗ (eq_bool y10 x10) ⊗ (eq_bool y11 x11) ⊗
- (eq_bool y12 x12) ⊗ (eq_bool y13 x13)));
- nrewrite > (symmetric_eqb8 x1 y1);
- nrewrite > (symmetric_eqb8 x2 y2);
- nrewrite > (symmetric_eqw16 x3 y3);
- nrewrite > (symmetric_eqw16 x4 y4);
- nrewrite > (symmetric_eqw16 x5 y5);
- nrewrite > (symmetric_eqw16 x6 y6);
- nrewrite > (symmetric_eqw16 x7 y7);
- nrewrite > (symmetric_eqbool x8 y8);
- nrewrite > (symmetric_eqbool x9 y9);
- nrewrite > (symmetric_eqbool x10 y10);
- nrewrite > (symmetric_eqbool x11 y11);
- nrewrite > (symmetric_eqbool x12 y12);
- nrewrite > (symmetric_eqbool x13 y13);
- napply refl_eq.
-nqed.
-
-nlemma eqaluHC05_to_eq : ∀alu1,alu2.eq_alu_HC05 alu1 alu2 = true → alu1 = alu2.
- #alu1; #alu2;
- ncases alu1;
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
- ncases alu2;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
- nchange in H:(%) with (
- ((eq_b8 x1 y1) ⊗ (eq_b8 x2 y2) ⊗
- (eq_w16 x3 y3) ⊗ (eq_w16 x4 y4) ⊗
- (eq_w16 x5 y5) ⊗ (eq_w16 x6 y6) ⊗
- (eq_w16 x7 y7) ⊗ (eq_bool x8 y8) ⊗
- (eq_bool x9 y9) ⊗ (eq_bool x10 y10) ⊗
- (eq_bool x11 y11) ⊗ (eq_bool x12 y12) ⊗
- (eq_bool x13 y13)) = true);
- nrewrite > (eqbool_to_eq … (andb_true_true_r … H));
- nletin H1 ≝ (andb_true_true_l … H);
- nrewrite > (eqbool_to_eq x12 y12 (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 > (eqbool_to_eq … (andb_true_true_r … H4));
- nletin H5 ≝ (andb_true_true_l … H4);
- nrewrite > (eqbool_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 > (eqb8_to_eq … (andb_true_true_r … H11));
- nrewrite > (eqb8_to_eq … (andb_true_true_l … H11));
- napply refl_eq.
-nqed.
-
-nlemma eq_to_eqaluHC05 : ∀alu1,alu2.alu1 = alu2 → eq_alu_HC05 alu1 alu2 = true.
- #alu1; #alu2;
- ncases alu1;
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
- ncases alu2;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13; #H;
- nrewrite > (aluHC05_destruct_1 … H);
- nrewrite > (aluHC05_destruct_2 … H);
- nrewrite > (aluHC05_destruct_3 … H);
- nrewrite > (aluHC05_destruct_4 … H);
- nrewrite > (aluHC05_destruct_5 … H);
- nrewrite > (aluHC05_destruct_6 … H);
- nrewrite > (aluHC05_destruct_7 … H);
- nrewrite > (aluHC05_destruct_8 … H);
- nrewrite > (aluHC05_destruct_9 … H);
- nrewrite > (aluHC05_destruct_10 … H);
- nrewrite > (aluHC05_destruct_11 … H);
- nrewrite > (aluHC05_destruct_12 … H);
- nrewrite > (aluHC05_destruct_13 … H);
- nchange with (
- ((eq_b8 y1 y1) ⊗ (eq_b8 y2 y2) ⊗
- (eq_w16 y3 y3) ⊗ (eq_w16 y4 y4) ⊗
- (eq_w16 y5 y5) ⊗ (eq_w16 y6 y6) ⊗
- (eq_w16 y7 y7) ⊗ (eq_bool y8 y8) ⊗
- (eq_bool y9 y9) ⊗ (eq_bool y10 y10) ⊗
- (eq_bool y11 y11) ⊗ (eq_bool y12 y12) ⊗
- (eq_bool y13 y13)) = true);
- nrewrite > (eq_to_eqb8 y1 y1 (refl_eq …));
- nrewrite > (eq_to_eqb8 y2 y2 (refl_eq …));
- nrewrite > (eq_to_eqw16 y3 y3 (refl_eq …));
- nrewrite > (eq_to_eqw16 y4 y4 (refl_eq …));
- nrewrite > (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_eqbool y8 y8 (refl_eq …));
- nrewrite > (eq_to_eqbool y9 y9 (refl_eq …));
- nrewrite > (eq_to_eqbool y10 y10 (refl_eq …));
- nrewrite > (eq_to_eqbool y11 y11 (refl_eq …));
- nrewrite > (eq_to_eqbool y12 y12 (refl_eq …));
- nrewrite > (eq_to_eqbool y13 y13 (refl_eq …));
- napply refl_eq.
-nqed.
-
-nlemma aluHC08_destruct_1 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
- mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 = mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 →
- x1 = y1.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
- nchange with (match mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12
- with [ mk_alu_HC08 a _ _ _ _ _ _ _ _ _ _ _ ⇒ x1 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluHC08_destruct_2 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
- mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 = mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 →
- x2 = y2.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
- nchange with (match mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12
- with [ mk_alu_HC08 _ a _ _ _ _ _ _ _ _ _ _ ⇒ x2 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluHC08_destruct_3 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
- mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 = mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 →
- x3 = y3.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
- nchange with (match mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12
- with [ mk_alu_HC08 _ _ a _ _ _ _ _ _ _ _ _ ⇒ x3 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluHC08_destruct_4 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
- mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 = mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 →
- x4 = y4.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
- nchange with (match mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12
- with [ mk_alu_HC08 _ _ _ a _ _ _ _ _ _ _ _ ⇒ x4 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluHC08_destruct_5 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
- mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 = mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 →
- x5 = y5.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
- nchange with (match mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12
- with [ mk_alu_HC08 _ _ _ _ a _ _ _ _ _ _ _ ⇒ x5 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluHC08_destruct_6 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
- mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 = mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 →
- x6 = y6.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
- nchange with (match mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12
- with [ mk_alu_HC08 _ _ _ _ _ a _ _ _ _ _ _ ⇒ x6 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluHC08_destruct_7 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
- mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 = mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 →
- x7 = y7.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
- nchange with (match mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12
- with [ mk_alu_HC08 _ _ _ _ _ _ a _ _ _ _ _ ⇒ x7 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluHC08_destruct_8 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
- mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 = mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 →
- x8 = y8.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
- nchange with (match mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12
- with [ mk_alu_HC08 _ _ _ _ _ _ _ a _ _ _ _ ⇒ x8 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluHC08_destruct_9 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
- mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 = mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 →
- x9 = y9.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
- nchange with (match mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12
- with [ mk_alu_HC08 _ _ _ _ _ _ _ _ a _ _ _ ⇒ x9 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluHC08_destruct_10 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
- mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 = mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 →
- x10 = y10.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
- nchange with (match mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12
- with [ mk_alu_HC08 _ _ _ _ _ _ _ _ _ a _ _ ⇒ x10 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluHC08_destruct_11 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
- mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 = mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 →
- x11 = y11.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
- nchange with (match mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12
- with [ mk_alu_HC08 _ _ _ _ _ _ _ _ _ _ a _ ⇒ x11 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluHC08_destruct_12 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12.
- mk_alu_HC08 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 = mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 →
- x12 = y12.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
- nchange with (match mk_alu_HC08 y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12
- with [ mk_alu_HC08 _ _ _ _ _ _ _ _ _ _ _ a ⇒ x12 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma symmetric_eqaluHC08 : symmetricT alu_HC08 bool eq_alu_HC08.
- #alu1; #alu2;
- ncases alu1;
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
- ncases alu2;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12;
- nchange with (
- ((eq_b8 x1 y1) ⊗ (eq_b8 x2 y2) ⊗ (eq_b8 x3 y3) ⊗ (eq_w16 x4 y4) ⊗
- (eq_w16 x5 y5) ⊗ (eq_bool x6 y6) ⊗ (eq_bool x7 y7) ⊗ (eq_bool x8 y8) ⊗
- (eq_bool x9 y9) ⊗ (eq_bool x10 y10) ⊗ (eq_bool x11 y11) ⊗ (eq_bool x12 y12)) =
- ((eq_b8 y1 x1) ⊗ (eq_b8 y2 x2) ⊗ (eq_b8 y3 x3) ⊗ (eq_w16 y4 x4) ⊗
- (eq_w16 y5 x5) ⊗ (eq_bool y6 x6) ⊗ (eq_bool y7 x7) ⊗ (eq_bool y8 x8) ⊗
- (eq_bool y9 x9) ⊗ (eq_bool y10 x10) ⊗ (eq_bool y11 x11) ⊗ (eq_bool y12 x12)));
- nrewrite > (symmetric_eqb8 x1 y1);
- nrewrite > (symmetric_eqb8 x2 y2);
- nrewrite > (symmetric_eqb8 x3 y3);
- nrewrite > (symmetric_eqw16 x4 y4);
- nrewrite > (symmetric_eqw16 x5 y5);
- nrewrite > (symmetric_eqbool x6 y6);
- nrewrite > (symmetric_eqbool x7 y7);
- nrewrite > (symmetric_eqbool x8 y8);
- nrewrite > (symmetric_eqbool x9 y9);
- nrewrite > (symmetric_eqbool x10 y10);
- nrewrite > (symmetric_eqbool x11 y11);
- nrewrite > (symmetric_eqbool x12 y12);
- napply refl_eq.
-nqed.
-
-nlemma eqaluHC08_to_eq : ∀alu1,alu2.eq_alu_HC08 alu1 alu2 = true → alu1 = alu2.
- #alu1; #alu2;
- ncases alu1;
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
- ncases alu2;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
- nchange in H:(%) with (
- ((eq_b8 x1 y1) ⊗ (eq_b8 x2 y2) ⊗ (eq_b8 x3 y3) ⊗ (eq_w16 x4 y4) ⊗
- (eq_w16 x5 y5) ⊗ (eq_bool x6 y6) ⊗ (eq_bool x7 y7) ⊗ (eq_bool x8 y8) ⊗
- (eq_bool x9 y9) ⊗ (eq_bool x10 y10) ⊗ (eq_bool x11 y11) ⊗ (eq_bool x12 y12)) = 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 … H1));
- 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 > (eqbool_to_eq … (andb_true_true_r … H4));
- nletin H5 ≝ (andb_true_true_l … H4);
- nrewrite > (eqbool_to_eq … (andb_true_true_r … H5));
- nletin H6 ≝ (andb_true_true_l … H5);
- nrewrite > (eqbool_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 > (eqb8_to_eq … (andb_true_true_r … H9));
- nletin H10 ≝ (andb_true_true_l … H9);
- nrewrite > (eqb8_to_eq … (andb_true_true_r … H10));
- nrewrite > (eqb8_to_eq … (andb_true_true_l … H10));
- napply refl_eq.
-nqed.
-
-nlemma eq_to_eqaluHC08 : ∀alu1,alu2.alu1 = alu2 → eq_alu_HC08 alu1 alu2 = true.
- #alu1; #alu2;
- ncases alu1;
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12;
- ncases alu2;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #H;
- nrewrite > (aluHC08_destruct_1 … H);
- nrewrite > (aluHC08_destruct_2 … H);
- nrewrite > (aluHC08_destruct_3 … H);
- nrewrite > (aluHC08_destruct_4 … H);
- nrewrite > (aluHC08_destruct_5 … H);
- nrewrite > (aluHC08_destruct_6 … H);
- nrewrite > (aluHC08_destruct_7 … H);
- nrewrite > (aluHC08_destruct_8 … H);
- nrewrite > (aluHC08_destruct_9 … H);
- nrewrite > (aluHC08_destruct_10 … H);
- nrewrite > (aluHC08_destruct_11 … H);
- nrewrite > (aluHC08_destruct_12 … H);
- nchange with (
- ((eq_b8 y1 y1) ⊗ (eq_b8 y2 y2) ⊗ (eq_b8 y3 y3) ⊗ (eq_w16 y4 y4) ⊗
- (eq_w16 y5 y5) ⊗ (eq_bool y6 y6) ⊗ (eq_bool y7 y7) ⊗ (eq_bool y8 y8) ⊗
- (eq_bool y9 y9) ⊗ (eq_bool y10 y10) ⊗ (eq_bool y11 y11) ⊗ (eq_bool y12 y12)) = 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_eqw16 y4 y4 (refl_eq …));
- nrewrite > (eq_to_eqw16 y5 y5 (refl_eq …));
- nrewrite > (eq_to_eqbool y6 y6 (refl_eq …));
- nrewrite > (eq_to_eqbool y7 y7 (refl_eq …));
- nrewrite > (eq_to_eqbool y8 y8 (refl_eq …));
- nrewrite > (eq_to_eqbool y9 y9 (refl_eq …));
- nrewrite > (eq_to_eqbool y10 y10 (refl_eq …));
- nrewrite > (eq_to_eqbool y11 y11 (refl_eq …));
- nrewrite > (eq_to_eqbool y12 y12 (refl_eq …));
- napply refl_eq.
-nqed.
-
-nlemma aluRS08_destruct_1 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8.
- mk_alu_RS08 x1 x2 x3 x4 x5 x6 x7 x8 = mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8 →
- x1 = y1.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
- nchange with (match mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8
- with [ mk_alu_RS08 a _ _ _ _ _ _ _ ⇒ x1 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluRS08_destruct_2 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8.
- mk_alu_RS08 x1 x2 x3 x4 x5 x6 x7 x8 = mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8 →
- x2 = y2.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
- nchange with (match mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8
- with [ mk_alu_RS08 _ a _ _ _ _ _ _ ⇒ x2 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluRS08_destruct_3 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8.
- mk_alu_RS08 x1 x2 x3 x4 x5 x6 x7 x8 = mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8 →
- x3 = y3.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
- nchange with (match mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8
- with [ mk_alu_RS08 _ _ a _ _ _ _ _ ⇒ x3 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluRS08_destruct_4 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8.
- mk_alu_RS08 x1 x2 x3 x4 x5 x6 x7 x8 = mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8 →
- x4 = y4.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
- nchange with (match mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8
- with [ mk_alu_RS08 _ _ _ a _ _ _ _ ⇒ x4 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluRS08_destruct_5 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8.
- mk_alu_RS08 x1 x2 x3 x4 x5 x6 x7 x8 = mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8 →
- x5 = y5.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
- nchange with (match mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8
- with [ mk_alu_RS08 _ _ _ _ a _ _ _ ⇒ x5 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluRS08_destruct_6 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8.
- mk_alu_RS08 x1 x2 x3 x4 x5 x6 x7 x8 = mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8 →
- x6 = y6.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
- nchange with (match mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8
- with [ mk_alu_RS08 _ _ _ _ _ a _ _ ⇒ x6 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluRS08_destruct_7 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8.
- mk_alu_RS08 x1 x2 x3 x4 x5 x6 x7 x8 = mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8 →
- x7 = y7.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
- nchange with (match mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8
- with [ mk_alu_RS08 _ _ _ _ _ _ a _ ⇒ x7 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma aluRS08_destruct_8 :
-∀x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8.
- mk_alu_RS08 x1 x2 x3 x4 x5 x6 x7 x8 = mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8 →
- x8 = y8.
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
- nchange with (match mk_alu_RS08 y1 y2 y3 y4 y5 y6 y7 y8
- with [ mk_alu_RS08 _ _ _ _ _ _ _ a ⇒ x8 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma symmetric_eqaluRS08 : symmetricT alu_RS08 bool eq_alu_RS08.
- #alu1; #alu2;
- ncases alu1;
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
- ncases alu2;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8;
- nchange with (
- ((eq_b8 x1 y1) ⊗ (eq_w16 x2 y2) ⊗
- (eq_w16 x3 y3) ⊗ (eq_w16 x4 y4) ⊗
- (eq_b8 x5 y5) ⊗ (eq_b8 x6 y6) ⊗
- (eq_bool x7 y7) ⊗ (eq_bool x8 y8)) =
- ((eq_b8 y1 x1) ⊗ (eq_w16 y2 x2) ⊗
- (eq_w16 y3 x3) ⊗ (eq_w16 y4 x4) ⊗
- (eq_b8 y5 x5) ⊗ (eq_b8 y6 x6) ⊗
- (eq_bool y7 x7) ⊗ (eq_bool y8 x8)));
- nrewrite > (symmetric_eqb8 x1 y1);
- nrewrite > (symmetric_eqw16 x2 y2);
- nrewrite > (symmetric_eqw16 x3 y3);
- nrewrite > (symmetric_eqw16 x4 y4);
- nrewrite > (symmetric_eqb8 x5 y5);
- nrewrite > (symmetric_eqb8 x6 y6);
- nrewrite > (symmetric_eqbool x7 y7);
- nrewrite > (symmetric_eqbool x8 y8);
- napply refl_eq.
-nqed.
-
-nlemma eqaluRS08_to_eq : ∀alu1,alu2.eq_alu_RS08 alu1 alu2 = true → alu1 = alu2.
- #alu1; #alu2;
- ncases alu1;
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
- ncases alu2;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
- nchange in H:(%) with (
- ((eq_b8 x1 y1) ⊗ (eq_w16 x2 y2) ⊗
- (eq_w16 x3 y3) ⊗ (eq_w16 x4 y4) ⊗
- (eq_b8 x5 y5) ⊗ (eq_b8 x6 y6) ⊗
- (eq_bool x7 y7) ⊗ (eq_bool x8 y8)) = 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 … H1));
- nletin H2 ≝ (andb_true_true_l … H1);
- nrewrite > (eqb8_to_eq … (andb_true_true_r … H2));
- nletin H3 ≝ (andb_true_true_l … H2);
- nrewrite > (eqb8_to_eq … (andb_true_true_r … H3));
- nletin H4 ≝ (andb_true_true_l … H3);
- nrewrite > (eqw16_to_eq … (andb_true_true_r … H4));
- nletin H5 ≝ (andb_true_true_l … H4);
- nrewrite > (eqw16_to_eq … (andb_true_true_r … H5));
- nletin H6 ≝ (andb_true_true_l … H5);
- nrewrite > (eqw16_to_eq … (andb_true_true_r … H6));
- nrewrite > (eqb8_to_eq … (andb_true_true_l … H6));
- napply refl_eq.
-nqed.
-
-nlemma eq_to_eqaluRS08 : ∀alu1,alu2.alu1 = alu2 → eq_alu_RS08 alu1 alu2 = true.
- #alu1; #alu2;
- ncases alu1;
- #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8;
- ncases alu2;
- #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #H;
- nrewrite > (aluRS08_destruct_1 … H);
- nrewrite > (aluRS08_destruct_2 … H);
- nrewrite > (aluRS08_destruct_3 … H);
- nrewrite > (aluRS08_destruct_4 … H);
- nrewrite > (aluRS08_destruct_5 … H);
- nrewrite > (aluRS08_destruct_6 … H);
- nrewrite > (aluRS08_destruct_7 … H);
- nrewrite > (aluRS08_destruct_8 … H);
- nchange with (
- ((eq_b8 y1 y1) ⊗ (eq_w16 y2 y2) ⊗
- (eq_w16 y3 y3) ⊗ (eq_w16 y4 y4) ⊗
- (eq_b8 y5 y5) ⊗ (eq_b8 y6 y6) ⊗
- (eq_bool y7 y7) ⊗ (eq_bool y8 y8)) = true);
- nrewrite > (eq_to_eqb8 y1 y1 (refl_eq …));
- nrewrite > (eq_to_eqw16 y2 y2 (refl_eq …));
- nrewrite > (eq_to_eqw16 y3 y3 (refl_eq …));
- nrewrite > (eq_to_eqw16 y4 y4 (refl_eq …));
- nrewrite > (eq_to_eqb8 y5 y5 (refl_eq …));
- nrewrite > (eq_to_eqb8 y6 y6 (refl_eq …));
- nrewrite > (eq_to_eqbool y7 y7 (refl_eq …));
- nrewrite > (eq_to_eqbool y8 y8 (refl_eq …));
- napply refl_eq.
-nqed.
-
-nlemma symmetric_eqclk : ∀mcu,clk1,clk2.eq_clk mcu clk1 clk2 = eq_clk mcu clk2 clk1.
- #mcu; #clk1; #clk2;
- ncases clk1;
- ncases clk2;
- ##[ ##1: napply refl_eq
- ##| ##2,3: nnormalize; #H; napply refl_eq
- ##| ##4: #p1; ncases p1; #x1; #x2; #x3; #x4; #x5;
- #p2; ncases p2; #y1; #y2; #y3; #y4; #y5;
- nchange with (
- ((eq_b8 y1 x1) ⊗ (eq_anyop ? y2 x2) ⊗ (eq_instrmode y3 x3) ⊗ (eq_b8 y4 x4) ⊗ (eq_w16 y5 x5)) =
- ((eq_b8 x1 y1) ⊗ (eq_anyop ? x2 y2) ⊗ (eq_instrmode x3 y3) ⊗ (eq_b8 x4 y4) ⊗ (eq_w16 x5 y5)));
- nrewrite > (symmetric_eqb8 x1 y1);
- nrewrite > (symmetric_eqanyop ? x2 y2);
- nrewrite > (symmetric_eqinstrmode x3 y3);
- nrewrite > (symmetric_eqb8 x4 y4);
- nrewrite > (symmetric_eqw16 x5 y5);
- napply refl_eq
- ##]
-nqed.
-
-nlemma eqclk_to_eq : ∀mcu,clk1,clk2.eq_clk mcu clk1 clk2 = true → clk1 = clk2.
- #mcu; #clk1; #clk2;
- ncases clk1;
- ncases clk2;
- ##[ ##1: nnormalize; #H; napply refl_eq
- ##| ##2,3: nnormalize; #H; #H1; napply (bool_destruct … H1)
- ##| ##4: #p1; ncases p1; #x1; #x2; #x3; #x4; #x5;
- #p2; ncases p2; #y1; #y2; #y3; #y4; #y5; #H;
- nchange in H:(%) with (
- ((eq_b8 y1 x1) ⊗ (eq_anyop ? y2 x2) ⊗ (eq_instrmode y3 x3) ⊗ (eq_b8 y4 x4) ⊗ (eq_w16 y5 x5)) = true);
- nrewrite > (eqw16_to_eq … (andb_true_true_r … H));
- nletin H1 ≝ (andb_true_true_l … H);
- nrewrite > (eqb8_to_eq … (andb_true_true_r … H1));
- nletin H2 ≝ (andb_true_true_l … H1);
- nrewrite > (eqinstrmode_to_eq … (andb_true_true_r … H2));
- nletin H3 ≝ (andb_true_true_l … H2);
- nrewrite > (eqanyop_to_eq … (andb_true_true_r … H3));
- nrewrite > (eqb8_to_eq … (andb_true_true_l … H3));
- napply refl_eq
- ##]
-nqed.
-
-nlemma eq_to_eqclk : ∀mcu,clk1,clk2.clk1 = clk2 → eq_clk mcu clk1 clk2 = true.
- #mcu; #clk1; #clk2;
- ncases clk1;
- ncases clk2;
- ##[ ##1: nnormalize; #H; napply refl_eq
- ##| ##2: nnormalize; #p; #H1; nelim (option_destruct_none_some … H1)
- ##| ##3: nnormalize; #p; #H1; nelim (option_destruct_some_none … H1)
- ##| ##4: #p1; ncases p1; #x1; #x2; #x3; #x4; #x5;
- #p2; ncases p2; #y1; #y2; #y3; #y4; #y5; #H;
- nrewrite > (quintuple_destruct_1 … (option_destruct_some_some … H));
- nrewrite > (quintuple_destruct_2 … (option_destruct_some_some … H));
- nrewrite > (quintuple_destruct_3 … (option_destruct_some_some … H));
- nrewrite > (quintuple_destruct_4 … (option_destruct_some_some … H));
- nrewrite > (quintuple_destruct_5 … (option_destruct_some_some … H));
- nchange with (
- ((eq_b8 x1 x1) ⊗ (eq_anyop ? x2 x2) ⊗ (eq_instrmode x3 x3) ⊗ (eq_b8 x4 x4) ⊗ (eq_w16 x5 x5)) = true);
- nrewrite > (eq_to_eqb8 x1 x1 (refl_eq …));
- nrewrite > (eq_to_eqanyop mcu x2 x2 (refl_eq ? x2));
- nrewrite > (eq_to_eqinstrmode x3 x3 (refl_eq …));
- nrewrite > (eq_to_eqb8 x4 x4 (refl_eq …));
- nrewrite > (eq_to_eqw16 x5 x5 (refl_eq …));
- nnormalize;
- napply refl_eq
- ##]
-nqed.
-
-nlemma symmetric_forallmemoryranged :
-∀t.∀chk1,chk2:aux_chk_type t.∀mem1,mem2:aux_mem_type t.∀addrl.
- forall_memory_ranged t chk1 chk2 mem1 mem2 addrl =
- forall_memory_ranged t chk2 chk1 mem2 mem1 addrl.
- #t; #chk1; #chk2; #mem1; #mem2; #addrl;
- napply (list_ind word16 … addrl);
- ##[ ##1: nnormalize; napply refl_eq
- ##| ##2: #a; #l; #H;
- nchange with (
- ((eq_option byte8 (mem_read t mem1 chk1 a)
- (mem_read t mem2 chk2 a) eq_b8) ⊗
- (forall_memory_ranged t chk1 chk2 mem1 mem2 l)) =
- ((eq_option byte8 (mem_read t mem2 chk2 a)
- (mem_read t mem1 chk1 a) eq_b8) ⊗
- (forall_memory_ranged t chk2 chk1 mem2 mem1 l)));
- nrewrite > H;
- nrewrite > (symmetric_eqoption ? (mem_read t mem1 chk1 a) (mem_read t mem2 chk2 a) eq_b8 symmetric_eqb8);
- napply refl_eq
- ##]
-nqed.
-
-nlemma anystatus_destruct_1 :
-∀m,t.∀x1,x2,x3,x4,y1,y2,y3,y4.
- mk_any_status m t x1 x2 x3 x4 = mk_any_status m t y1 y2 y3 y4 →
- x1 = y1.
- #m; #t;
- #x1; #x2; #x3; #x4;
- #y1; #y2; #y3; #y4; #H;
- nchange with (match mk_any_status m t y1 y2 y3 y4
- with [ mk_any_status a _ _ _ ⇒ x1 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma anystatus_destruct_2 :
-∀m,t.∀x1,x2,x3,x4,y1,y2,y3,y4.
- mk_any_status m t x1 x2 x3 x4 = mk_any_status m t y1 y2 y3 y4 →
- x2 = y2.
- #m; #t;
- #x1; #x2; #x3; #x4;
- #y1; #y2; #y3; #y4; #H;
- nchange with (match mk_any_status m t y1 y2 y3 y4
- with [ mk_any_status _ a _ _ ⇒ x2 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma anystatus_destruct_3 :
-∀m,t.∀x1,x2,x3,x4,y1,y2,y3,y4.
- mk_any_status m t x1 x2 x3 x4 = mk_any_status m t y1 y2 y3 y4 →
- x3 = y3.
- #m; #t;
- #x1; #x2; #x3; #x4;
- #y1; #y2; #y3; #y4; #H;
- nchange with (match mk_any_status m t y1 y2 y3 y4
- with [ mk_any_status _ _ a _ ⇒ x3 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma anystatus_destruct_4 :
-∀m,t.∀x1,x2,x3,x4,y1,y2,y3,y4.
- mk_any_status m t x1 x2 x3 x4 = mk_any_status m t y1 y2 y3 y4 →
- x4 = y4.
- #m; #t;
- #x1; #x2; #x3; #x4;
- #y1; #y2; #y3; #y4; #H;
- nchange with (match mk_any_status m t y1 y2 y3 y4
- with [ mk_any_status _ _ _ a ⇒ x4 = a ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma symmetric_eqstatus :
-∀addrl:list word16.∀m:mcu_type.∀t:memory_impl.∀s1,s2:any_status m t.
- eq_status m t s1 s2 addrl = eq_status m t s2 s1 addrl.
- #addrl; #m;
- ncases m; #t; #s1;
- ##[ ##1: ncases s1; #x1; #x2; #x3; #x4;
- #s2; ncases s2; #y1; #y2; #y3; #y4;
- nchange with (
- ((eq_alu_HC05 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk HC05 x4 y4)) =
- ((eq_alu_HC05 y1 x1) ⊗ (forall_memory_ranged t y3 x3 y2 x2 addrl) ⊗ (eq_clk HC05 y4 x4)));
- nrewrite > (symmetric_eqaluHC05 x1 y1)
- ##| ##2,3: ncases s1; #x1; #x2; #x3; #x4;
- #s2; ncases s2; #y1; #y2; #y3; #y4;
- nchange with (
- ((eq_alu_HC08 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) =
- ((eq_alu_HC08 y1 x1) ⊗ (forall_memory_ranged t y3 x3 y2 x2 addrl) ⊗ (eq_clk ? y4 x4)));
- nrewrite > (symmetric_eqaluHC08 x1 y1)
- ##| ##4: ncases s1; #x1; #x2; #x3; #x4;
- #s2; ncases s2; #y1; #y2; #y3; #y4;
- nchange with (
- ((eq_alu_RS08 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk RS08 x4 y4)) =
- ((eq_alu_RS08 y1 x1) ⊗ (forall_memory_ranged t y3 x3 y2 x2 addrl) ⊗ (eq_clk RS08 y4 x4)));
- nrewrite > (symmetric_eqaluRS08 x1 y1)
- ##]
- nrewrite > (symmetric_forallmemoryranged t x3 y3 x2 y2 addrl);
- nrewrite > (symmetric_eqclk ? x4 y4);
- napply refl_eq.
-nqed.
-
-nlemma eqstatus_to_eq :
-∀addrl:list word16.∀m:mcu_type.∀t:memory_impl.∀s1,s2:any_status m t.
- (eq_status m t s1 s2 addrl = true) →
- ((alu m t s1 = alu m t s2) ∧
- (clk_desc m t s1 = clk_desc m t s2) ∧
- ((forall_memory_ranged t (chk_desc m t s1) (chk_desc m t s2)
- (mem_desc m t s1) (mem_desc m t s2) addrl) = true)).
- #addrl; #m; #t;
- ncases m; #s1;
- ##[ ##1: ncases s1; #x1; #x2; #x3; #x4;
- #s2; ncases s2; #y1; #y2; #y3; #y4; #H;
- nchange in H:(%) with (
- ((eq_alu_HC05 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
- nrewrite > (eqaluHC05_to_eq … (andb_true_true_l … (andb_true_true_l … H)))
- ##| ##2,3: ncases s1; #x1; #x2; #x3; #x4;
- #s2; ncases s2; #y1; #y2; #y3; #y4; #H;
- nchange in H:(%) with (
- ((eq_alu_HC08 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
- nrewrite > (eqaluHC08_to_eq … (andb_true_true_l … (andb_true_true_l … H)))
- ##| ##4: ncases s1; #x1; #x2; #x3; #x4;
- #s2; ncases s2; #y1; #y2; #y3; #y4; #H;
- nchange in H:(%) with (
- ((eq_alu_RS08 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
- nrewrite > (eqaluRS08_to_eq … (andb_true_true_l … (andb_true_true_l … H)))
- ##]
- nchange with ((y1 = y1) ∧ (x4 = y4) ∧ (forall_memory_ranged t x3 y3 x2 y2 addrl = true));
- nrewrite > (andb_true_true_r … (andb_true_true_l … H));
- nrewrite > (eqclk_to_eq … (andb_true_true_r … H));
- napply (conj … (conj … (refl_eq …) (refl_eq …)) (refl_eq …)).
-nqed.
-
-nlemma eq_to_eqstatus_strong :
-∀addrl:list word16.∀m:mcu_type.∀t:memory_impl.∀s1,s2:any_status m t.
- s1 = s2 → (eq_status m t s1 s2 addrl = true).
- #addrl; #m; #t;
- ncases m;
- ##[ ##1: #s1; ncases s1; #x1; #x2; #x3; #x4;
- #s2; ncases s2; #y1; #y2; #y3; #y4; #H;
- nchange with (
- ((eq_alu_HC05 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
- nrewrite > (anystatus_destruct_1 … H);
- nrewrite > (eq_to_eqaluHC05 y1 y1 (refl_eq …))
- ##| ##2,3: #s1; ncases s1; #x1; #x2; #x3; #x4;
- #s2; ncases s2; #y1; #y2; #y3; #y4; #H;
- nchange with (
- ((eq_alu_HC08 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
- nrewrite > (anystatus_destruct_1 … H);
- nrewrite > (eq_to_eqaluHC08 y1 y1 (refl_eq …))
- ##| ##4: #s1; ncases s1; #x1; #x2; #x3; #x4;
- #s2; ncases s2; #y1; #y2; #y3; #y4; #H;
- nchange with (
- ((eq_alu_RS08 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
- nrewrite > (anystatus_destruct_1 … H);
- nrewrite > (eq_to_eqaluRS08 y1 y1 (refl_eq …))
- ##]
- nrewrite > (anystatus_destruct_2 … H);
- nrewrite > (anystatus_destruct_3 … H);
- nrewrite > (anystatus_destruct_4 … H);
- nrewrite > (eq_to_eqclk ? y4 y4 (refl_eq …));
- nchange with ((forall_memory_ranged … ⊗ true) =true);
- nrewrite > (symmetric_andbool (forall_memory_ranged t y3 y3 y2 y2 addrl) true);
- nchange with (forall_memory_ranged … = true);
- napply (list_ind word16 … addrl);
- ##[ ##1,3,5,7: nnormalize; napply refl_eq
- ##| ##2,4,6,8: #a; #l'; #H;
- nchange with (
- ((eq_option byte8 (mem_read t y2 y3 a)
- (mem_read t y2 y3 a) eq_b8) ⊗
- (forall_memory_ranged t y3 y3 y2 y2 l')) = true);
- nrewrite > H;
- nrewrite > (eq_to_eqoption ? (mem_read t y2 y3 a) (mem_read t y2 y3 a) eq_b8 eq_to_eqb8 (refl_eq …));
- nnormalize;
- napply refl_eq
- ##]
-nqed.
-
-nlemma eq_to_eqstatus_weak :
-∀addrl:list word16.∀m:mcu_type.∀t:memory_impl.∀s1,s2:any_status m t.
- (alu m t s1 = alu m t s2) →
- (clk_desc m t s1 = clk_desc m t s2) →
- ((forall_memory_ranged t (chk_desc m t s1) (chk_desc m t s2)
- (mem_desc m t s1) (mem_desc m t s2) addrl) = true) →
- (eq_status m t s1 s2 addrl = true).
- #addrl; #m; #t;
- ncases m;
- ##[ ##1: #s1; ncases s1; #x1; #x2; #x3; #x4;
- #s2; ncases s2; #y1; #y2; #y3; #y4; #H; #H1; #H2;
- nchange with (((eq_alu_HC05 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
- nchange in H:(%) with (x1 = y1);
- nrewrite > H;
- nrewrite > (eq_to_eqaluHC05 y1 y1 (refl_eq …))
- ##| ##2,3: #s1; ncases s1; #x1; #x2; #x3; #x4;
- #s2; ncases s2; #y1; #y2; #y3; #y4; #H; #H1; #H2;
- nchange with (((eq_alu_HC08 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
- nchange in H:(%) with (x1 = y1);
- nrewrite > H;
- nrewrite > (eq_to_eqaluHC08 y1 y1 (refl_eq …))
- ##| ##4: #s1; ncases s1; #x1; #x2; #x3; #x4;
- #s2; ncases s2; #y1; #y2; #y3; #y4; #H; #H1; #H2;
- nchange with (((eq_alu_RS08 x1 y1) ⊗ (forall_memory_ranged t x3 y3 x2 y2 addrl) ⊗ (eq_clk ? x4 y4)) = true);
- nchange in H:(%) with (x1 = y1);
- nrewrite > H;
- nrewrite > (eq_to_eqaluRS08 y1 y1 (refl_eq …))
- ##]
- nchange in H2:(%) with (forall_memory_ranged t x3 y3 x2 y2 addrl = true);
- nrewrite > H2;
- nchange in H1:(%) with (x4 = y4);
- nrewrite > H1;
- nrewrite > (eq_to_eqclk ? y4 y4 (refl_eq …));
- nnormalize;
- napply refl_eq.
-nqed.
projects / helm.git / blobdiff