Some understanding of the notion of proof is necessary for any mathematician, if for nothing else, then at least for the communicability of mathematical results: publication rests on the understanding that proofs can be made as explicit as to be routinely checkable for correctness.
In cats it's been used to create glowing kittens with no other traits, just proof that it can be made to work.
The proof of the proposition can be made in a similar way to the proof in [9, Proposition 3.1].
Most mathematicians would agree that, by contrast, if a proof's implicit steps can be made explicit by an expert, then the gap is merely one of exposition, and the proof should be considered complete and correct.
In every detail, in proportion and fit, a coat in charcoal English wool, with off-white facing in the front flap — the better to flatter the face — was proof that masculine tailoring can be made feminine and modern.
In that case, don't ask for the entire $1.5 million up front; if you do, the value of your company will be based on the fact that you (currently) have no hard proof that a working prototype can be made, much less that anyone would want to distribute it.
The recent news from the United Nations Food and Agriculture Organization (FAO) that world hunger dropped by over 100 million in the last decade is proof of the progress that can be made with strong commitments from governments, civil society, academic and research institutions, private sector, and farmers themselves.
Good proofs of an intaglio plate can be made by plaster casting, for fine plaster of paris will pick up the most delicate details.
