fsatz, nsatz_solve_nonzero

1 files changed, 12 insertions, 5 deletions

diff --git a/src/Spec/CompleteEdwardsCurve.v b/src/Spec/CompleteEdwardsCurve.v
index e081ded1e..d475f78c2 100644
--- a/src/Spec/CompleteEdwardsCurve.v
+++ b/src/Spec/CompleteEdwardsCurve.v
@@ -13,13 +13,14 @@ Module E.
     Local Infix "=" := Feq : type_scope. Local Notation "a <> b" := (not (a = b)) : type_scope.
     Local Notation "0" := Fzero.  Local Notation "1" := Fone.
     Local Infix "+" := Fadd. Local Infix "*" := Fmul.
-    Local Infix "-" := Fsub. Local Infix "/" := Fdiv.
+    Local Infix "-" := Fsub.
     Local Notation "x ^ 2" := (x*x) (at level 30).
+    Local Notation "n / d" := (fst (Fdiv n d, (_:(d <> 0)))). (* force nonzero d *)
 
     Context {a d: F}.
     Class twisted_edwards_params :=
       {
-        char_gt_2 : 1 + 1 <> 0;
+        char_gt_2 : forall p : BinNums.positive, BinPos.Pos.le p 2 -> Pre.ZtoR (BinNums.Zpos p) <> 0;
         nonzero_a : a <> 0;
         square_a : exists sqrt_a, sqrt_a^2 = a;
         nonsquare_d : forall x, x^2 <> d
@@ -28,15 +29,20 @@ Module E.
 
     Definition point := { P | let '(x,y) := P in a*x^2 + y^2 = 1 + d*x^2*y^2 }.
     Definition coordinates (P:point) : (F*F) := proj1_sig P.
+    Definition eq (P Q:point) :=
+      fst (coordinates P) = fst (coordinates Q) /\
+      snd (coordinates P) = snd (coordinates Q).
 
     Program Definition zero : point := (0, 1).
-    Next Obligation. auto using Pre.zeroOnCurve. Defined.
+    Next Obligation. eauto using Pre.onCurve_zero. Qed.
 
     Program Definition add (P1 P2:point) : point :=
       let x1y1 := coordinates P1 in let x1 := fst x1y1 in let y1 := snd x1y1 in
       let x2y2 := coordinates P2 in let x2 := fst x2y2 in let y2 := snd x2y2 in
         (((x1*y2  +  y1*x2)/(1 + d*x1*x2*y1*y2)) , ((y1*y2 - a*x1*x2)/(1 - d*x1*x2*y1*y2))).
-    Next Obligation. destruct P1 as [[??]?], P2 as [[??]?], H; auto using Pre.add_onCurve. Defined.
+    Next Obligation. destruct P1 as [[??]?], P2 as [[??]?], H. eauto using Pre.denominator_nonzero_x. Qed.
+    Next Obligation. destruct P1 as [[??]?], P2 as [[??]?], H; eauto using Pre.denominator_nonzero_y. Qed.
+    Next Obligation. destruct P1 as [[??]?], P2 as [[??]?], H; eauto using Pre.onCurve_add. Qed.
 
     Fixpoint mul (n:nat) (P : point) : point :=
       match n with
@@ -47,5 +53,6 @@ Module E.
 End E.
 
 Delimit Scope E_scope with E.
+Infix "=" := E.eq : E_scope.
 Infix "+" := E.add : E_scope.
-Infix "*" := E.mul : E_scope.
+Infix "*" := E.mul : E_scope.
\ No newline at end of file