I think a proof of not-not-X[1] is more apt to be called “a co-proof of X” (which implies X if you [locally] assume the law of the excluded middle).
Or, weaker, very strong [evidence of]/[argument for] not-not-X.
I think a proof of not-not-X[1] is more apt to be called “a co-proof of X” (which implies X if you [locally] assume the law of the excluded middle).
Or, weaker, very strong [evidence of]/[argument for] not-not-X.