1 files changed, 38 insertions, 0 deletions
diff --git a/src/CompleteEdwardsCurve/ExtendedCoordinatesIssue.v b/src/CompleteEdwardsCurve/ExtendedCoordinatesIssue.v
new file mode 100644
index 000000000..8d24f2cd2
--- /dev/null
+++ b/src/CompleteEdwardsCurve/ExtendedCoordinatesIssue.v
@@ -0,0 +1,38 @@
+Require Import Crypto.ModularArithmetic.PrimeFieldTheorems.
+Require Import Crypto.Spec.CompleteEdwardsCurve.
+
+Section ExtendedCoordinates.
+  Local Open Scope F_scope.
+
+  Context {prm:TwistedEdwardsParams}.
+  Context {p:BinInt.Z} {p_eq_q:p = q}.
+  Lemma prime_p : Znumtheory.prime p.
+    rewrite p_eq_q; exact prime_q.
+  Qed.
+
+  Add Field Ffield_Z : (@Ffield_theory p prime_p)
+    (morphism (@Fring_morph p),
+     preprocess [Fpreprocess],
+     postprocess [Fpostprocess],
+     constants [Fconstant],
+     div (@Fmorph_div_theory p),
+     power_tac (@Fpower_theory p) [Fexp_tac]). 
+
+  Lemma biggerFraction : forall XP YP ZP XQ YQ ZQ d : F q, 
+   ZQ <> 0 ->
+   ZP <> 0 ->
+   ZP * ZQ * ZP * ZQ + d * XP * XQ * YP * YQ <> 0 ->
+   ZP * ZToField 2 * ZQ * (ZP * ZQ) + XP * YP * ZToField 2 * d * (XQ * YQ) <> 0 ->
+   ZP * ZToField 2 * ZQ * (ZP * ZQ) - XP * YP * ZToField 2 * d * (XQ * YQ) <> 0 ->
+
+   ((YP + XP) * (YQ + XQ) - (YP - XP) * (YQ - XQ)) *
+   (ZP * ZToField 2 * ZQ - XP * YP / ZP * ZToField 2 * d * (XQ * YQ / ZQ)) /
+   ((ZP * ZToField 2 * ZQ - XP * YP / ZP * ZToField 2 * d * (XQ * YQ / ZQ)) *
+    (ZP * ZToField 2 * ZQ + XP * YP / ZP * ZToField 2 * d * (XQ * YQ / ZQ))) =
+   (XP / ZP * (YQ / ZQ) + YP / ZP * (XQ / ZQ)) / (1 + d * (XP / ZP) * (XQ / ZQ) * (YP / ZP) * (YQ / ZQ)).
+  Proof.
+    rewrite <-p_eq_q.
+    intros.
+    abstract (field; assumption).
+  Qed.
+End ExtendedCoordinates.
+\ No newline at end of file