[a1369209993]

No, what you've observed is the (IIRC the terminology) converse, namely:

It is not sufficient merely to test a program; you have to prove it correct too.

In addition, it is not sufficient merely to prove a program correct; you have to test it too.

In summary, you have to both prove a program correct, and test it; skipping either will result in buggy garbage.

[joshuamorton]

Grandparent is correct. If you've proven the behavior correct, you don't need to test. The proof is the test. This is usually only true in languages-that-are-proof-assistants (idris). In the cases above, they hadn't actually formally proven the behavior correct.