freescale porting to ng, work in progress

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

diff --git a/helm/software/matita/contribs/ng_assembly/freescale/nat_lemmas.ma b/helm/software/matita/contribs/ng_assembly/freescale/nat_lemmas.ma
index fde0972e4c9b1f3d9f32eb840ec32628681932f7..70b9bbbb90418046b7ec8fe8f7a5dc75ec06d288 100644 (file)
--- a/helm/software/matita/contribs/ng_assembly/freescale/nat_lemmas.ma
+++ b/helm/software/matita/contribs/ng_assembly/freescale/nat_lemmas.ma
@@ -31,7 +31,7 @@ include "freescale/nat.ma".
 (* NATURALI *)
 (* ******** *)
 
-nlemma nat_destruct : ∀n1,n2:nat.S n1 = S n2 → n1 = n2.
+nlemma nat_destruct_S_S : ∀n1,n2:nat.S n1 = S n2 → n1 = n2.
  #n1; #n2; #H;
  nchange with (match S n2 with [ O ⇒ False | S a ⇒ n1 = a ]);
  nrewrite < H;
@@ -55,7 +55,7 @@ nlemma nat_destruct_S_0 : ∀n:nat.S n = O → False.
  napply I.
 nqed.
 
-nlemma bsymmetric_eqnat : boolSymmetric nat eq_nat.
+nlemma symmetric_eqnat : symmetricT nat bool eq_nat.
  nnormalize;
  #n1;
  nelim n1;
@@ -73,7 +73,7 @@ nlemma bsymmetric_eqnat : boolSymmetric nat eq_nat.
           ##| ##2: #n4; napply (H n4)
           ##]
  ##]
-nqed.  
+nqed.
 
 nlemma eq_to_eqnat : ∀n1,n2:nat.n1 = n2 → eq_nat n1 n2 = true.
  #n1;
@@ -89,7 +89,7 @@ nlemma eq_to_eqnat : ∀n1,n2:nat.n1 = n2 → eq_nat n1 n2 = true.
           nnormalize;
           ##[ ##1: #H1; nelim (nat_destruct_S_0 ? H1)
           ##| ##2: #n4; #H1;
-                   napply (H n4 (nat_destruct ?? H1))
+                   napply (H n4 (nat_destruct_S_S ?? H1))
           ##]
  ##]
 nqed. 
@@ -101,12 +101,12 @@ nlemma eqnat_to_eq : ∀n1,n2:nat.(eq_nat n1 n2 = true → n1 = n2).
           nelim n2;
           nnormalize;
           ##[ ##1: #H; napply (refl_eq ??)
-          ##| ##2: #n3; #H; #H1; nelim (bool_destruct_false_true H1)
+          ##| ##2: #n3; #H; #H1; napply (bool_destruct ?? (O = S n3) H1) 
           ##]
  ##| ##2: #n2; #H; #n3; #H1;
           ncases n3 in H1:(%) ⊢ %;
           nnormalize;
-          ##[ ##1: #H1; nelim (bool_destruct_false_true H1)
+          ##[ ##1: #H1; napply (bool_destruct ?? (S n2 = O) H1)
           ##| ##2: #n4; #H1;
                    nrewrite > (H n4 H1);
                    napply (refl_eq ??)