freescale porting to ng, work in progress

[helm.git] / helm / software / matita / contribs / ng_assembly / freescale / prod_lemmas.ma

diff --git a/helm/software/matita/contribs/ng_assembly/freescale/prod_lemmas.ma b/helm/software/matita/contribs/ng_assembly/freescale/prod_lemmas.ma
index d95af89a67a15d3e9938caed9c242d8f0e3d0f79..6d666ca0dd3361eb29334a5a1d7a83df7938188b 100644 (file)
--- a/helm/software/matita/contribs/ng_assembly/freescale/prod_lemmas.ma
+++ b/helm/software/matita/contribs/ng_assembly/freescale/prod_lemmas.ma
@@ -51,16 +51,17 @@ nlemma pair_destruct_2 :
  napply (refl_eq ??).
 nqed.
 
-nlemma bsymmetric_eqpair :
+nlemma symmetric_eqpair :
 ∀T1,T2:Type.∀p1,p2:ProdT T1 T2.
 ∀f1:T1 → T1 → bool.∀f2:T2 → T2 → bool.
- (boolSymmetric T1 f1) →
- (boolSymmetric T2 f2) →
+ (symmetricT T1 bool f1) →
+ (symmetricT T2 bool f2) →
  (eq_pair T1 T2 p1 p2 f1 f2 = eq_pair T1 T2 p2 p1 f1 f2).
  #T1; #T2; #p1; #p2; #f1; #f2; #H; #H1;
- ncases p1;
- ncases p2;
- #x2; #y2; #x1; #y1;
+ napply (ProdT_ind T1 T2 ?? p1);
+ #x1; #y1;
+ napply (ProdT_ind T1 T2 ?? p2);
+ #x2; #y2;
  nnormalize;
  nrewrite > (H x1 x2);
  ncases (f1 x2 x1);
@@ -77,9 +78,10 @@ nlemma eq_to_eqpair :
  (∀y1,y2:T2.y1 = y2 → f2 y1 y2 = true) →
  (p1 = p2 → eq_pair T1 T2 p1 p2 f1 f2 = true).
  #T1; #T2; #p1; #p2; #f1; #f2; #H1; #H2;
- ncases p1;
- ncases p2;
- #x2; #y2; #x1; #y1; #H;
+ napply (ProdT_ind T1 T2 ?? p1);
+ #x1; #y1;
+ napply (ProdT_ind T1 T2 ?? p2);
+ #x2; #y2; #H;
  nnormalize;
  nrewrite > (H1 ?? (pair_destruct_1 ?????? H));
  nnormalize;
@@ -94,15 +96,16 @@ nlemma eqpair_to_eq :
  (∀y1,y2:T2.f2 y1 y2 = true → y1 = y2) →
  (eq_pair T1 T2 p1 p2 f1 f2 = true → p1 = p2).
  #T1; #T2; #p1; #p2; #f1; #f2; #H1; #H2;
- ncases p1;
- ncases p2;
- #x2; #y2; #x1; #y1; #H;
+ napply (ProdT_ind T1 T2 ?? p1);
+ #x1; #y1;
+ napply (ProdT_ind T1 T2 ?? p2);
+ #x2; #y2; #H;
  nnormalize in H:(%);
  nletin K ≝ (H1 x1 x2);
  ncases (f1 x1 x2) in H:(%) K:(%);
  nnormalize;
  #H3;
- ##[ ##2: nelim (bool_destruct_false_true H3) ##]
+ ##[ ##2: napply (bool_destruct ??? H3) ##]
  #H4;
  nrewrite > (H4 (refl_eq ??));
  nrewrite > (H2 y1 y2 H3);
@@ -139,17 +142,18 @@ nlemma triple_destruct_3 :
  napply (refl_eq ??).
 nqed.
 
-nlemma bsymmetric_eqtriple :
+nlemma symmetric_eqtriple :
 ∀T1,T2,T3:Type.∀p1,p2:Prod3T T1 T2 T3.
 ∀f1:T1 → T1 → bool.∀f2:T2 → T2 → bool.∀f3:T3 → T3 → bool.
- (boolSymmetric T1 f1) →
- (boolSymmetric T2 f2) →
- (boolSymmetric T3 f3) →
+ (symmetricT T1 bool f1) →
+ (symmetricT T2 bool f2) →
+ (symmetricT T3 bool f3) →
  (eq_triple T1 T2 T3 p1 p2 f1 f2 f3 = eq_triple T1 T2 T3 p2 p1 f1 f2 f3).
  #T1; #T2; #T3; #p1; #p2; #f1; #f2; #f3; #H; #H1; #H2;
- ncases p1;
- ncases p2;
- #x2; #y2; #z2; #x1; #y1; #z1;
+ napply (Prod3T_ind T1 T2 T3 ?? p1);
+ #x1; #y1; #z1;
+ napply (Prod3T_ind T1 T2 T3 ?? p2);
+ #x2; #y2; #z2;
  nnormalize;
  nrewrite > (H x1 x2);
  ncases (f1 x2 x1);
@@ -172,9 +176,10 @@ nlemma eq_to_eqtriple :
  (∀z1,z2:T3.z1 = z2 → f3 z1 z2 = true) →
  (p1 = p2 → eq_triple T1 T2 T3 p1 p2 f1 f2 f3 = true).
  #T1; #T2; #T3; #p1; #p2; #f1; #f2; #f3; #H1; #H2; #H3;
- ncases p1;
- ncases p2;
- #x2; #y2; #z2; #x1; #y1; #z1; #H;
+ napply (Prod3T_ind T1 T2 T3 ?? p1);
+ #x1; #y1; #z1;
+ napply (Prod3T_ind T1 T2 T3 ?? p2);
+ #x2; #y2; #z2; #H;
  nnormalize;
  nrewrite > (H1 ?? (triple_destruct_1 ????????? H));
  nnormalize;
@@ -192,18 +197,19 @@ nlemma eqtriple_to_eq :
  (∀z1,z2:T3.f3 z1 z2 = true → z1 = z2) →
  (eq_triple T1 T2 T3 p1 p2 f1 f2 f3 = true → p1 = p2).
  #T1; #T2; #T3; #p1; #p2; #f1; #f2; #f3; #H1; #H2; #H3;
- ncases p1;
- ncases p2;
- #x2; #y2; #z2; #x1; #y1; #z1; #H;
+ napply (Prod3T_ind T1 T2 T3 ?? p1);
+ #x1; #y1; #z1;
+ napply (Prod3T_ind T1 T2 T3 ?? p2);
+ #x2; #y2; #z2; #H;
  nnormalize in H:(%);
  nletin K ≝ (H1 x1 x2);
  ncases (f1 x1 x2) in H:(%) K:(%);
  nnormalize;
- ##[ ##2: #H4; nelim (bool_destruct_false_true H4) ##]
+ ##[ ##2: #H4; napply (bool_destruct ??? H4) ##]
  nletin K1 ≝ (H2 y1 y2);
  ncases (f2 y1 y2) in K1:(%) ⊢ %;
  nnormalize;
- ##[ ##2: #H4; #H5; nelim (bool_destruct_false_true H5) ##]
+ ##[ ##2: #H4; #H5; napply (bool_destruct ??? H5) ##]
  #H4; #H5; #H6;
  nrewrite > (H4 (refl_eq ??));
  nrewrite > (H6 (refl_eq ??));
@@ -251,18 +257,19 @@ nlemma quadruple_destruct_4 :
  napply (refl_eq ??).
 nqed.
 
-nlemma bsymmetric_eqquadruple :
+nlemma symmetric_eqquadruple :
 ∀T1,T2,T3,T4:Type.∀p1,p2:Prod4T T1 T2 T3 T4.
 ∀f1:T1 → T1 → bool.∀f2:T2 → T2 → bool.∀f3:T3 → T3 → bool.∀f4:T4 → T4 → bool.
- (boolSymmetric T1 f1) →
- (boolSymmetric T2 f2) →
- (boolSymmetric T3 f3) →
- (boolSymmetric T4 f4) →
+ (symmetricT T1 bool f1) →
+ (symmetricT T2 bool f2) →
+ (symmetricT T3 bool f3) →
+ (symmetricT T4 bool f4) →
  (eq_quadruple T1 T2 T3 T4 p1 p2 f1 f2 f3 f4 = eq_quadruple T1 T2 T3 T4 p2 p1 f1 f2 f3 f4).
  #T1; #T2; #T3; #T4; #p1; #p2; #f1; #f2; #f3; #f4; #H; #H1; #H2; #H3;
- ncases p1;
- ncases p2;
- #x2; #y2; #z2; #v2; #x1; #y1; #z1; #v1;
+ napply (Prod4T_ind T1 T2 T3 T4 ?? p1);
+ #x1; #y1; #z1; #v1;
+ napply (Prod4T_ind T1 T2 T3 T4 ?? p2);
+ #x2; #y2; #z2; #v2;
  nnormalize;
  nrewrite > (H x1 x2);
  ncases (f1 x2 x1);
@@ -291,9 +298,10 @@ nlemma eq_to_eqquadruple :
  (∀v1,v2:T4.v1 = v2 → f4 v1 v2 = true) →
  (p1 = p2 → eq_quadruple T1 T2 T3 T4 p1 p2 f1 f2 f3 f4 = true).
  #T1; #T2; #T3; #T4; #p1; #p2; #f1; #f2; #f3; #f4; #H1; #H2; #H3; #H4;
- ncases p1;
- ncases p2;
- #x2; #y2; #z2; #v2; #x1; #y1; #z1; #v1; #H;
+ napply (Prod4T_ind T1 T2 T3 T4 ?? p1);
+ #x1; #y1; #z1; #v1;
+ napply (Prod4T_ind T1 T2 T3 T4 ?? p2);
+ #x2; #y2; #z2; #v2; #H;
  nnormalize;
  nrewrite > (H1 ?? (quadruple_destruct_1 ???????????? H));
  nnormalize;
@@ -314,22 +322,23 @@ nlemma eqquadruple_to_eq :
  (∀v1,v2:T4.f4 v1 v2 = true → v1 = v2) →
  (eq_quadruple T1 T2 T3 T4 p1 p2 f1 f2 f3 f4 = true → p1 = p2).
  #T1; #T2; #T3; #T4; #p1; #p2; #f1; #f2; #f3; #f4; #H1; #H2; #H3; #H4;
- ncases p1;
- ncases p2;
- #x2; #y2; #z2; #v2; #x1; #y1; #z1; #v1; #H;
+ napply (Prod4T_ind T1 T2 T3 T4 ?? p1);
+ #x1; #y1; #z1; #v1;
+ napply (Prod4T_ind T1 T2 T3 T4 ?? p2);
+ #x2; #y2; #z2; #v2; #H;
  nnormalize in H:(%);
  nletin K ≝ (H1 x1 x2);
  ncases (f1 x1 x2) in H:(%) K:(%);
  nnormalize;
- ##[ ##2: #H5; nelim (bool_destruct_false_true H5) ##]
+ ##[ ##2: #H5; napply (bool_destruct ??? H5) ##]
  nletin K1 ≝ (H2 y1 y2);
  ncases (f2 y1 y2) in K1:(%) ⊢ %;
  nnormalize;
- ##[ ##2: #H5; #H6; nelim (bool_destruct_false_true H6) ##]
+ ##[ ##2: #H5; #H6; napply (bool_destruct ??? H6) ##]
  nletin K2 ≝ (H3 z1 z2);
  ncases (f3 z1 z2) in K2:(%) ⊢ %;
  nnormalize;
- ##[ ##2: #H5; #H6; #H7; nelim (bool_destruct_false_true H7) ##]
+ ##[ ##2: #H5; #H6; #H7; napply (bool_destruct ??? H7) ##]
  #H5; #H6; #H7; #H8;
  nrewrite > (H5 (refl_eq ??));
  nrewrite > (H6 (refl_eq ??));
@@ -388,19 +397,20 @@ nlemma quintuple_destruct_5 :
  napply (refl_eq ??).
 nqed.
 
-nlemma bsymmetric_eqquintuple :
+nlemma symmetric_eqquintuple :
 ∀T1,T2,T3,T4,T5:Type.∀p1,p2:Prod5T T1 T2 T3 T4 T5.
 ∀f1:T1 → T1 → bool.∀f2:T2 → T2 → bool.∀f3:T3 → T3 → bool.∀f4:T4 → T4 → bool.∀f5:T5 → T5 → bool.
- (boolSymmetric T1 f1) →
- (boolSymmetric T2 f2) →
- (boolSymmetric T3 f3) →
- (boolSymmetric T4 f4) →
- (boolSymmetric T5 f5) →
+ (symmetricT T1 bool f1) →
+ (symmetricT T2 bool f2) →
+ (symmetricT T3 bool f3) →
+ (symmetricT T4 bool f4) →
+ (symmetricT T5 bool f5) →
  (eq_quintuple T1 T2 T3 T4 T5 p1 p2 f1 f2 f3 f4 f5 = eq_quintuple T1 T2 T3 T4 T5 p2 p1 f1 f2 f3 f4 f5).
  #T1; #T2; #T3; #T4; #T5; #p1; #p2; #f1; #f2; #f3; #f4; #f5; #H; #H1; #H2; #H3; #H4;
- ncases p1;
- ncases p2;
- #x2; #y2; #z2; #v2; #w2; #x1; #y1; #z1; #v1; #w1;
+ napply (Prod5T_ind T1 T2 T3 T4 T5 ?? p1);
+ #x1; #y1; #z1; #v1; #w1;
+ napply (Prod5T_ind T1 T2 T3 T4 T5 ?? p2);
+ #x2; #y2; #z2; #v2; #w2;
  nnormalize;
  nrewrite > (H x1 x2);
  ncases (f1 x2 x1);
@@ -435,9 +445,10 @@ nlemma eq_to_eqquintuple :
  (∀w1,w2:T5.w1 = w2 → f5 w1 w2 = true) →
  (p1 = p2 → eq_quintuple T1 T2 T3 T4 T5 p1 p2 f1 f2 f3 f4 f5 = true).
  #T1; #T2; #T3; #T4; #T5; #p1; #p2; #f1; #f2; #f3; #f4; #f5; #H1; #H2; #H3; #H4; #H5;
- ncases p1;
- ncases p2;
- #x2; #y2; #z2; #v2; #w2; #x1; #y1; #z1; #v1; #w1; #H;
+ napply (Prod5T_ind T1 T2 T3 T4 T5 ?? p1);
+ #x1; #y1; #z1; #v1; #w1;
+ napply (Prod5T_ind T1 T2 T3 T4 T5 ?? p2);
+ #x2; #y2; #z2; #v2; #w2; #H;
  nnormalize;
  nrewrite > (H1 ?? (quintuple_destruct_1 ??????????????? H));
  nnormalize;
@@ -461,26 +472,27 @@ nlemma eqquintuple_to_eq :
  (∀w1,w2:T5.f5 w1 w2 = true → w1 = w2) →
  (eq_quintuple T1 T2 T3 T4 T5 p1 p2 f1 f2 f3 f4 f5 = true → p1 = p2).
  #T1; #T2; #T3; #T4; #T5; #p1; #p2; #f1; #f2; #f3; #f4; #f5; #H1; #H2; #H3; #H4; #H5;
- ncases p1;
- ncases p2;
- #x2; #y2; #z2; #v2; #w2; #x1; #y1; #z1; #v1; #w1; #H;
+ napply (Prod5T_ind T1 T2 T3 T4 T5 ?? p1);
+ #x1; #y1; #z1; #v1; #w1;
+ napply (Prod5T_ind T1 T2 T3 T4 T5 ?? p2);
+ #x2; #y2; #z2; #v2; #w2; #H;
  nnormalize in H:(%);
  nletin K ≝ (H1 x1 x2);
  ncases (f1 x1 x2) in H:(%) K:(%);
  nnormalize;
- ##[ ##2: #H6; nelim (bool_destruct_false_true H6) ##]
+ ##[ ##2: #H6; napply (bool_destruct ??? H6) ##]
  nletin K1 ≝ (H2 y1 y2);
  ncases (f2 y1 y2) in K1:(%) ⊢ %;
  nnormalize;
- ##[ ##2: #H6; #H7; nelim (bool_destruct_false_true H7) ##]
+ ##[ ##2: #H6; #H7; napply (bool_destruct ??? H7) ##]
  nletin K2 ≝ (H3 z1 z2);
  ncases (f3 z1 z2) in K2:(%) ⊢ %;
  nnormalize;
- ##[ ##2: #H6; #H7; #H8; nelim (bool_destruct_false_true H8) ##]
+ ##[ ##2: #H6; #H7; #H8; napply (bool_destruct ??? H8) ##]
  nletin K3 ≝ (H4 v1 v2);
  ncases (f4 v1 v2) in K3:(%) ⊢ %;
  nnormalize;
- ##[ ##2: #H6; #H7; #H8; #H9; nelim (bool_destruct_false_true H9) ##]
+ ##[ ##2: #H6; #H7; #H8; #H9; napply (bool_destruct ??? H9) ##]
  #H6; #H7; #H8; #H9; #H10;
  nrewrite > (H6 (refl_eq ??));
  nrewrite > (H7 (refl_eq ??));