Fix failure note `to_str` implementation

* Serialize the level to something a little more useful for a failure note
  struct
* Update tests accordingly
diff --git a/src/librustc_errors/emitter.rs b/src/librustc_errors/emitter.rs
index 0ce69ee..5214806 100644
--- a/src/librustc_errors/emitter.rs
+++ b/src/librustc_errors/emitter.rs
@@ -1144,15 +1144,18 @@
                 buffer.prepend(0, " ", Style::NoStyle);
             }
             draw_note_separator(&mut buffer, 0, max_line_num_len + 1);
-            let level_str = level.to_string();
-            if !level_str.is_empty() {
-                buffer.append(0, &level_str, Style::MainHeaderMsg);
-                buffer.append(0, ": ", Style::NoStyle);
+            if *level != Level::FailureNote {
+                let level_str = level.to_string();
+                if !level_str.is_empty() {
+                    buffer.append(0, &level_str, Style::MainHeaderMsg);
+                    buffer.append(0, ": ", Style::NoStyle);
+                }
             }
             self.msg_to_buffer(&mut buffer, msg, max_line_num_len, "note", None);
         } else {
             let level_str = level.to_string();
-            if !level_str.is_empty() {
+            // The failure note level itself does not provide any useful diagnostic information
+            if *level != Level::FailureNote && !level_str.is_empty() {
                 buffer.append(0, &level_str, Style::Level(level.clone()));
             }
             // only render error codes, not lint codes
@@ -1161,7 +1164,7 @@
                 buffer.append(0, &code, Style::Level(level.clone()));
                 buffer.append(0, "]", Style::Level(level.clone()));
             }
-            if !level_str.is_empty() {
+            if *level != Level::FailureNote && !level_str.is_empty() {
                 buffer.append(0, ": ", header_style);
             }
             for &(ref text, _) in msg.iter() {
diff --git a/src/librustc_errors/lib.rs b/src/librustc_errors/lib.rs
index c1fba41..8b543be 100644
--- a/src/librustc_errors/lib.rs
+++ b/src/librustc_errors/lib.rs
@@ -833,7 +833,7 @@
             Warning => "warning",
             Note => "note",
             Help => "help",
-            FailureNote => "",
+            FailureNote => "failure-note",
             Cancelled => panic!("Shouldn't call on cancelled error"),
         }
     }
diff --git a/src/test/ui/json-short.stderr b/src/test/ui/json-short.stderr
index dffbdb7..549de0d2 100644
--- a/src/test/ui/json-short.stderr
+++ b/src/test/ui/json-short.stderr
@@ -15,5 +15,5 @@
 "}
 {"message":"aborting due to previous error","code":null,"level":"error","spans":[],"children":[],"rendered":"error: aborting due to previous error
 "}
-{"message":"For more information about this error, try `rustc --explain E0601`.","code":null,"level":"","spans":[],"children":[],"rendered":"For more information about this error, try `rustc --explain E0601`.
+{"message":"For more information about this error, try `rustc --explain E0601`.","code":null,"level":"failure-note","spans":[],"children":[],"rendered":"For more information about this error, try `rustc --explain E0601`.
 "}
diff --git a/src/test/ui/lint/use_suggestion_json.stderr b/src/test/ui/lint/use_suggestion_json.stderr
index c7c53ab..678c888 100644
--- a/src/test/ui/lint/use_suggestion_json.stderr
+++ b/src/test/ui/lint/use_suggestion_json.stderr
@@ -412,7 +412,7 @@
 {
   "message": "For more information about this error, try `rustc --explain E0412`.",
   "code": null,
-  "level": "",
+  "level": "failure-note",
   "spans": [],
   "children": [],
   "rendered": "\u001b[0m\u001b[1mFor more information about this error, try `rustc --explain E0412`.\u001b[0m