Suggestion: output fewer errors for incorrectly implemented interface

TypeScript Version: nightly

Code

interface A {
    f(): void;
}
class B implements A {
    eff() {}
}

var b: B;
b.f();
b.f();
b.f();

Expected behavior:

src/a.ts(4,7): error TS2420: Class 'B' incorrectly implements interface 'A'.
  Property 'f' is missing in type 'B'.

Actual behavior:

src/a.ts(4,7): error TS2420: Class 'B' incorrectly implements interface 'A'.
  Property 'f' is missing in type 'B'.
src/a.ts(9,3): error TS2339: Property 'f' does not exist on type 'B'.
src/a.ts(10,3): error TS2339: Property 'f' does not exist on type 'B'.
src/a.ts(11,3): error TS2339: Property 'f' does not exist on type 'B'.

There can be an overwhelming number of missing-property errors if a commonly-used class mis-implements an interface it declares.

Start by reproducing the issue with the src/a.ts example using the TypeScript nightly compiler and compare the TS2420 and repeated TS2339 diagnostics. The change is complete when a class that incorrectly implements an interface does not produce an overwhelming number of redundant missing-property errors.