+ 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 decidable_aluHC05_aux1
+ : ∀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.
+ (x1 ≠ y1) →
+ (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; #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;
+ nnormalize; #H; #H1;
+ napply (H (aluHC05_destruct_1 … H1)).
+nqed.
+
+nlemma decidable_aluHC05_aux2
+ : ∀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.
+ (x2 ≠ y2) →
+ (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; #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;
+ nnormalize; #H; #H1;
+ napply (H (aluHC05_destruct_2 … H1)).
+nqed.
+
+nlemma decidable_aluHC05_aux3
+ : ∀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.
+ (x3 ≠ y3) →
+ (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; #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;
+ nnormalize; #H; #H1;
+ napply (H (aluHC05_destruct_3 … H1)).
+nqed.
+
+nlemma decidable_aluHC05_aux4
+ : ∀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.
+ (x4 ≠ y4) →
+ (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; #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;
+ nnormalize; #H; #H1;
+ napply (H (aluHC05_destruct_4 … H1)).
+nqed.
+
+nlemma decidable_aluHC05_aux5
+ : ∀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.
+ (x5 ≠ y5) →
+ (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; #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;
+ nnormalize; #H; #H1;
+ napply (H (aluHC05_destruct_5 … H1)).
+nqed.
+
+nlemma decidable_aluHC05_aux6
+ : ∀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.
+ (x6 ≠ y6) →
+ (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; #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;
+ nnormalize; #H; #H1;
+ napply (H (aluHC05_destruct_6 … H1)).
+nqed.
+
+nlemma decidable_aluHC05_aux7
+ : ∀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.
+ (x7 ≠ y7) →
+ (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; #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;
+ nnormalize; #H; #H1;
+ napply (H (aluHC05_destruct_7 … H1)).
+nqed.
+
+nlemma decidable_aluHC05_aux8
+ : ∀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.
+ (x8 ≠ y8) →
+ (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; #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;
+ nnormalize; #H; #H1;
+ napply (H (aluHC05_destruct_8 … H1)).
+nqed.
+
+nlemma decidable_aluHC05_aux9
+ : ∀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.
+ (x9 ≠ y9) →
+ (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; #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;
+ nnormalize; #H; #H1;
+ napply (H (aluHC05_destruct_9 … H1)).
+nqed.
+
+nlemma decidable_aluHC05_aux10
+ : ∀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.
+ (x10 ≠ y10) →
+ (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; #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;
+ nnormalize; #H; #H1;
+ napply (H (aluHC05_destruct_10 … H1)).
+nqed.
+
+nlemma decidable_aluHC05_aux11
+ : ∀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.
+ (x11 ≠ y11) →
+ (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; #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;
+ nnormalize; #H; #H1;
+ napply (H (aluHC05_destruct_11 … H1)).
+nqed.
+
+nlemma decidable_aluHC05_aux12
+ : ∀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.
+ (x12 ≠ y12) →
+ (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; #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;
+ nnormalize; #H; #H1;
+ napply (H (aluHC05_destruct_12 … H1)).
+nqed.
+
+nlemma decidable_aluHC05_aux13
+ : ∀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.
+ (x13 ≠ 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; #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;
+ nnormalize; #H; #H1;
+ napply (H (aluHC05_destruct_13 … H1)).
+nqed.
+
+nlemma decidable_aluHC05 : ∀x,y:alu_HC05.decidable (x = y).
+ #x; nelim x; #x1; #x2; #x3; #x4; #x5; #x6; #x7; #x8; #x9; #x10; #x11; #x12; #x13;
+ #y; nelim y; #y1; #y2; #y3; #y4; #y5; #y6; #y7; #y8; #y9; #y10; #y11; #y12; #y13;
+ nnormalize;
+ napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_b8 x1 y1) …);
+ ##[ ##2: #H; napply (or2_intro2 … (decidable_aluHC05_aux1 … H))
+ ##| ##1: #H; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_b8 x2 y2) …);
+ ##[ ##2: #H1; napply (or2_intro2 … (decidable_aluHC05_aux2 … H1))
+ ##| ##1: #H1; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_w16 x3 y3) …);
+ ##[ ##2: #H2; napply (or2_intro2 … (decidable_aluHC05_aux3 … H2))
+ ##| ##1: #H2; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_w16 x4 y4) …);
+ ##[ ##2: #H3; napply (or2_intro2 … (decidable_aluHC05_aux4 … H3))
+ ##| ##1: #H3; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_w16 x5 y5) …);
+ ##[ ##2: #H4; napply (or2_intro2 … (decidable_aluHC05_aux5 … H4))
+ ##| ##1: #H4; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_w16 x6 y6) …);
+ ##[ ##2: #H5; napply (or2_intro2 … (decidable_aluHC05_aux6 … H5))
+ ##| ##1: #H5; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_w16 x7 y7) …);
+ ##[ ##2: #H6; napply (or2_intro2 … (decidable_aluHC05_aux7 … H6))
+ ##| ##1: #H6; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_bool x8 y8) …);
+ ##[ ##2: #H7; napply (or2_intro2 … (decidable_aluHC05_aux8 … H7))
+ ##| ##1: #H7; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_bool x9 y9) …);
+ ##[ ##2: #H8; napply (or2_intro2 … (decidable_aluHC05_aux9 … H8))
+ ##| ##1: #H8; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_bool x10 y10) …);
+ ##[ ##2: #H9; napply (or2_intro2 … (decidable_aluHC05_aux10 … H9))
+ ##| ##1: #H9; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_bool x11 y11) …);
+ ##[ ##2: #H10; napply (or2_intro2 … (decidable_aluHC05_aux11 … H10))
+ ##| ##1: #H10; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_bool x12 y12) …);
+ ##[ ##2: #H11; napply (or2_intro2 … (decidable_aluHC05_aux12 … H11))
+ ##| ##1: #H11; napply (or2_elim (? = ?) (? ≠ ?) ? (decidable_bool x13 y13) …);
+ ##[ ##2: #H12; napply (or2_intro2 … (decidable_aluHC05_aux13 … H12))
+ ##| ##1: #H12; 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; napply (or2_intro1 (? = ?) (? ≠ ?) (refl_eq …))
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]
+ ##]