freescale translation (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 96bc15172b9f334b0f56c3c69b664c4e080bbce0..0c8c6e6339f8e8cb932b90277a73b39e1b27b030 100644 (file)
--- a/helm/software/matita/contribs/ng_assembly/freescale/prod_lemmas.ma
+++ b/helm/software/matita/contribs/ng_assembly/freescale/prod_lemmas.ma
@@ -58,9 +58,10 @@ nlemma bsymmetric_eqpair :
  (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;
@@ -94,9 +96,10 @@ 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:(%);
@@ -147,9 +150,10 @@ nlemma bsymmetric_eqtriple :
  (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;
@@ -192,9 +197,10 @@ 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:(%);
@@ -260,9 +266,10 @@ nlemma bsymmetric_eqquadruple :
  (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;
@@ -314,9 +322,10 @@ 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:(%);
@@ -398,9 +407,10 @@ nlemma bsymmetric_eqquintuple :
  (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;
@@ -461,9 +472,10 @@ 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:(%);