"proved a much lengthier task" or "was proved TO BE a much lengthier task"?

Question

But, though Æthelbert, king of Kent, was duly converted to Christianity and Augustine was soon able to establish the seat of his bishopric at Canterbury, the permanent establishment of Christianity throughout England proved a much lengthier task and one which required the active intervention of Celtic missionaries from Ireland and Scotland.
^{Book- David Daiches, A critical history of English literature Pg. No. 6.}

I think it should be:

The permanent establishment of Christianity was proved a much lengthier task.

or

The permanent establishment of Christianity was proved to be a much lengthier task.

But in the book it is written "the permanent establishment of Christianity throughout England proved a much lengthier task..."

Is this correct, only writing 'proved'?

Answer 1

Yes, it is perfectly correct. Proved to be = turned out to be

See this definition.

Prove can mean test as well as demonstrate the truth of.