In English language there is a beautiful colloquial usage, which describes the way a proof is done ie a "handwavy proof". A handwavy proof is a kind of proof, in which you use no/very little mathematical rigour and motivate the theorem by physical assumptions. Wiktionary defines handwavy in the following way:
Of a demonstration, proof, or explanation, missing important details or logical steps, perhaps instead appealing to common sense, tradition, intuition, or examples.
One could always say non-rigorous proof ie nicht strenger Beweis but that doesn't seem to describe the situation as nice as handwavy proof.