The phrase "after proving for" is not correct in standard written English.
It seems to be a misphrasing, possibly intended to convey a meaning related to demonstrating or establishing something.
Example: "After proving for the necessary conditions, we can proceed with the experiment."
Alternatives: "after establishing" or "after demonstrating".
Warwickshire's chances of winning the county championship may be fading, but the Bears remain on course for a one-day double after proving too strong for Kent in front of a desperately sparse crowd for a semi-final.
Roger Federer reached the last 16 at the Australian Open after proving too strong for Grigor Dimitrov in their highly-anticipated third-round match.
So, after proving this property for a Banach space, we know, without any characterization of the dual space, that it is super-reflexive, so reflexive as well.
Ball has previously been one of the president's top targets after proving insufficiently grateful for Trump's help in getting his son, UCLA player LiAngelo Ball, out of Chinese jail and later hotel detention for allegedly shoplifting.
But these qualities, after proving politically advantageous for decades, could become an albatross because of the state's shifting demographics and political leanings as the 84-year-old decides whether to seek a sixth term.
May all my most favorite players show up at Mike McKenzie's Tailgate & Party for a Purpose after they crush the Vikings, proving for one last friggin time why they are the Superbowl Champs.
She lost to a Republican two years later, but only after proving it was possible for a Democrat to win.
After proving the general result for the n th order case, we concentrate our work in the first order problem u ′ ( t ) + a u ( − t ) + b u ( t ) = h ( t ), for a.e. t ∈ R ; u ( t 0 ) = c, (2.5).
Rose found that even after proving their innocence, defendants imprisoned for crimes they didn't commit are sometimes told they have to plead guilty if they want to be released from jail.
After proving to be no challenge for the Huskies during the first 15 years of the rivalry which began in 1995, Notre Dame had owned the series lately, winning seven of the previous nine meetings.
