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.
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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.