In your base sentence, *There is no way*, the noun *way* is what determines what constructions may follow. *Way* takes (as we used to put it—today the technical term is *licenses*) the following constructions with the sense *[Subject] can prove X*

**Non-finite clauses**

- a way *to prove X*

- a way *of proving X*

- a way *for Subject to prove X*

**Finite clauses**

- a way *(that/in which) Subject can prove X*

- a way *(that/in which) X can be proven*

This is true whether your base sentence is *There is no way* or *There is a way* or *There may be a way* or *There are many ways* or any other variation on this theme: *way* determines what constructions are permissible.

But when you drop *no way* you change the entire structure of the sentence. The construction *There is*, by itself, can only take a noun phrase as its complement. None of these constructions will work.

The apparent counter-examples you cite belong to different structures:

To someone infected by the conspiracy theory virus it doesn't matter how much evidence there is to prove that 9/11 was indeed an attack ... *Once you unpack the relative clause, the relevant piece of the sentence boils down to ***There is evidence to prove that X**.

There is less evidence to support the supposition that Foster's death was a homicide than there is to prove that Nicole Brown Simpson was ... *Again, after unpacking, the relevant piece of the sentence boils down to ***There is more evidence to prove that X**.

**Evidence** performs the same role in both of these as *way* in your sentence, governing what constructions are permissible.

Also grammatically correct would be to finish the phrases with ... (to prove|of proving) (him|her|them|...) (right|wrong|[in]correct). – Will Crawford – 2019-12-27T13:34:45.767

1+1 However, all four are correct when

no wayis changed toa way. – StoneyB on hiatus – 2013-03-07T23:02:44.157@StoneyB: Yes, but the OP didn't suggest that possibility. :-) – None – 2013-03-07T23:03:43.913

3Then that is a deficiency on his part which should be remedied. Perhaps he doesn't know of the possibility and would be happy to be informed of it. :) – StoneyB on hiatus – 2013-03-07T23:06:48.003

Bill, on Internet there are several instances of "there is to prove that," among which it seems interesting the following (telegraph.co.uk) "... how much evidence there is to prove that 9/11 was indeed an attack planned and carried out by AQ." However there are others, also on The New York Times. – None – 2013-03-07T23:13:40.337

... "... the supposition that Foster's death was a homicide than there is to prove that Nicole Brown Simpson ..." one can read on The New York Times. – None – 2013-03-07T23:18:58.873

... in other words, it doesn't seem so rare to find that expression. – None – 2013-03-07T23:20:05.333

2@Carlo The NYT examples don't begin sentences; yours do. By the way, it would be easier to talk about these examples with either complete sentences or links to where complete sentences can be found. – snailplane – 2013-03-07T23:35:31.230

@Carlo: Two problems with your NYT examples. First, as snailplane points out, they are not complete sentences, merely snippets & structurally (syntactically) different from your four example sentences. Second, the NYT is a pay-to-read site after the first 10 articles in any given 30-day period from an initial click on a NYT article, so please copy & paste the full sentence (plus the previous one or two, if possible or relevant). – None – 2013-03-07T23:48:32.727

2@Carlo_R. The example you give is clearly syntactically different, as Bill says: it is a relative clause with a 'null-relativizer':

evidence [which] there is to prove that ...Translated into your structure this would beThere is evidence to prove that ...(orThere is evidence proving that ...). – StoneyB on hiatus – 2013-03-08T00:03:45.787