"unequivocally proves" is a correct and usable phrase in written English.
It can be used to emphasize that something is without a doubt or completely proven. Example: The DNA evidence presented in court unequivocally proves that the defendant is guilty of the crime.
By doing all the amazing things the "young old" are capable of – that huge swaths of them are doing already, largely unnoticed – and that (this is the nanny state bit) the science unequivocally proves older people should be doing, for their own health and wellbeing.
This unequivocally proves the proximity of the couple W124/E125 close to the pore mouth.
"This unequivocally proves there was sarin in Syria.
The final reveal - Tim noticing an inexplicable curvature in the seahorse pattern on the virginal of "The Music Lesson" - unequivocally proves that one of the most revered painters of Western civilization in fact DID NOT "paint," but rather traced shades of light radiating through lens and mirrors to capture hues and flavors that are unseeable and even unimaginable to other painters.
Inorganic arsenic (As) is a human carcinogen but has not been unequivocally proven carcinogenic in rodents.
"If Mr Maaßen sets out such claims, he must unequivocally prove them.
"We believe that the facts unequivocally proved a substantial breach by Mr. Drapkin.
"The medical harms or benefits have not been unequivocally proven," says the British Medical Association in its guidance for doctors.
However, it is challenging to design experiments that unequivocally prove the advantageous effects of regulated cell death on immunity.
But while markers can point to candidates, they can't unequivocally prove the identity of a stem cell.
But it exists in only a small percentage of cases, and without it there is almost no way for a prisoner to unequivocally prove his innocence.
