Move some lemmas

coq/Infra/RealRationalProps.v

@@ -165,31 +165,6 @@ Proof.
   unfold Qle_bool; auto.
 Qed.
 
-Lemma minAbs_positive_iv_is_lo a b:
-  (0 < a)%R ->
-  (a <= b)%R ->
-  RminAbsFun (a,b) = a.
-Proof.
-  intros; unfold RminAbsFun; simpl.
-  assert (0 < b)%R by lra.
-  assert (Rabs a = a)%R as Rabs_pos_a by (apply Rabs_right; lra).
-  assert (Rabs b = b)%R as Rabs_pos_b by (apply Rabs_right; lra).
-  rewrite Rabs_pos_a, Rabs_pos_b.
-  rewrite Rmin_left; lra.
-Qed.
-
-Lemma minAbs_negative_iv_is_hi a b:
-  (b < 0)%R ->
-  (a <= b)%R ->
-  (RminAbsFun (a,b) = - b)%R.
-Proof.
-  intros; unfold RminAbsFun; simpl.
-  assert (Rabs a = - a)%R as Rabs_neg_a by (apply Rabs_left; lra).
-  assert (Rabs b = - b)%R as Rabs_neg_b by (apply Rabs_left; lra).
-  rewrite Rabs_neg_a, Rabs_neg_b.
-  rewrite Rmin_right; lra.
-Qed.
-
 Lemma Q_case_div_to_R_case_div a b:
   (b < 0 \/ 0 < a)%Q ->
   (Q2R b < 0 \/ 0 < Q2R a)%R.

coq/IntervalArith.v

@@ -347,4 +347,30 @@ Proof.
   rewrite Rabs_minus_sym in abs_le.
   unfold Rabs in abs_le.
   destruct Rcase_abs in abs_le; try lra.
+Qed.
+
+
+Lemma minAbs_positive_iv_is_lo a b:
+  (0 < a)%R ->
+  (a <= b)%R ->
+  RminAbsFun (a,b) = a.
+Proof.
+  intros; unfold RminAbsFun; simpl.
+  assert (0 < b)%R by lra.
+  assert (Rabs a = a)%R as Rabs_pos_a by (apply Rabs_right; lra).
+  assert (Rabs b = b)%R as Rabs_pos_b by (apply Rabs_right; lra).
+  rewrite Rabs_pos_a, Rabs_pos_b.
+  rewrite Rmin_left; lra.
+Qed.
+
+Lemma minAbs_negative_iv_is_hi a b:
+  (b < 0)%R ->
+  (a <= b)%R ->
+  (RminAbsFun (a,b) = - b)%R.
+Proof.
+  intros; unfold RminAbsFun; simpl.
+  assert (Rabs a = - a)%R as Rabs_neg_a by (apply Rabs_left; lra).
+  assert (Rabs b = - b)%R as Rabs_neg_b by (apply Rabs_left; lra).
+  rewrite Rabs_neg_a, Rabs_neg_b.
+  rewrite Rmin_right; lra.
 Qed.
\ No newline at end of file