Original sentence: )"which was to be demonstrated"The abbreviation is often written at the bottom of a mathematical proof.quod gratis asseritur, gratis negatur"what is asserted without reason may be denied without reason"If no grounds have been given for an assertion, there is no need to provide grounds for contradicting it
Edited sentence: )"which was demonstrated"The abbreviation is often written at the bottom of a mathematical proof.quod gratis asseritur, gratis negatur"what is asserted without reason may be denied without reason"If no grounds have been given for an assertion, then there are no grounds needed to rejection it