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+Require Import Fappli_IEEE.
+Require Import Fappli_IEEE_bits.
+Require Import Floats.
+Require Import ZArith.
+Require Import Integers.
+
+(* Needed to break a circular reference after extraction *)
+Definition transform_quiet_pl :=
+  Eval unfold Float.transform_quiet_pl in Float.transform_quiet_pl.
+
+Program Definition default_pl : bool * nan_pl 53 := (true, nat_iter 51 xO xH).
+
+Definition binop_pl (pl1 pl2:binary64) : bool*nan_pl 53 :=
+  match pl1, pl2 with
+    | B754_nan s1 pl1, _ => (s1, transform_quiet_pl pl1)
+    | _, B754_nan s2 pl2 => (s2, transform_quiet_pl pl2)
+    | _, _ => default_pl
+  end.
+
+Theorem binop_propagate1: Float.binop_propagate1_prop binop_pl.
+Proof.
+  repeat intro. destruct f1, f2; try discriminate; simpl; reflexivity.
+Qed.
+
+Theorem binop_propagate2: Float.binop_propagate2_prop binop_pl.
+Proof.
+  repeat intro. destruct f1, f2, f3; try discriminate; simpl; reflexivity.
+Qed.