Make type_annotate_public_apis/omit_obvious_property_types incompatible

Change-Id: I6a703160772291f07e6df93cdc51df9ddebe0115
Reviewed-on: https://dart-review.googlesource.com/c/sdk/+/429662
Reviewed-by: Brian Wilkerson <brianwilkerson@google.com>
Commit-Queue: Erik Ernst <eernst@google.com>

pkg/linter/lib/src/rules/omit_obvious_property_types.dart

diff --git a/pkg/linter/lib/src/rules/omit_obvious_property_types.dart b/pkg/linter/lib/src/rules/omit_obvious_property_types.dart
index be4c19b..9137677 100644
--- a/pkg/linter/lib/src/rules/omit_obvious_property_types.dart
+++ b/pkg/linter/lib/src/rules/omit_obvious_property_types.dart
@@ -25,7 +25,10 @@
       LinterLintCode.omit_obvious_property_types;
 
   @override
-  List<String> get incompatibleRules => const ['always_specify_types'];
+  List<String> get incompatibleRules => const [
+    'always_specify_types',
+    'type_annotate_public_apis',
+  ];
 
   @override
   void registerNodeProcessors(

pkg/linter/lib/src/rules/type_annotate_public_apis.dart

diff --git a/pkg/linter/lib/src/rules/type_annotate_public_apis.dart b/pkg/linter/lib/src/rules/type_annotate_public_apis.dart
index ca9c554..af570b3 100644
--- a/pkg/linter/lib/src/rules/type_annotate_public_apis.dart
+++ b/pkg/linter/lib/src/rules/type_annotate_public_apis.dart
@@ -21,6 +21,9 @@
   DiagnosticCode get diagnosticCode => LinterLintCode.type_annotate_public_apis;
 
   @override
+  List<String> get incompatibleRules => const ['omit_obvious_property_types'];
+
+  @override
   void registerNodeProcessors(
     NodeLintRegistry registry,
     LinterContext context,