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 <[email protected]>
Commit-Queue: Erik Ernst <[email protected]>

Author: eernstg

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

@@ -25,7 +25,10 @@ class OmitObviousPropertyTypes extends LintRule {
       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

@@ -20,6 +20,9 @@ class TypeAnnotatePublicApis extends LintRule {
   @override
   DiagnosticCode get diagnosticCode => LinterLintCode.type_annotate_public_apis;
 
+  @override
+  List<String> get incompatibleRules => const ['omit_obvious_property_types'];
+
   @override
   void registerNodeProcessors(
     NodeLintRegistry registry,