The publisher, for example, sees proof of "the power of hope".
If the proof of a pudding is in the eating, and the proof of a rule is in the exceptions, where should we look for the proof of a philosophy?
Consider, for example, laws requiring proof of citizenship or photo ID to register or to vote.
For example, if every step of reasoning introduces a new source of error, how can we possibly improve our reliability – as we think we do – by proof-checking, filling in gaps in proofs, or consulting an expert, all of which add steps to our reasoning?
For example, a proof of B from A is considered valid, if every closed proof, which is obtained by replacing the open assumption A with a closed proof of A, is valid.
Companies can use this information to provide proof of legitimacy for products in pharmaceutical shipments, for example, and proof of authenticity for luxury goods.
Examples of hard instances can be found among the ones used for the proof of NP-completeness.
In radiological research, some felt that relevant outcomes could not be feasibly measured, for example if it necessitated surgical or autopsy proof.
Proof The proof of (i) is easily obtained; see for example, in [[5], Lemma 2.3].
For example, if you want a ferret, make sure you ferret-proof your room.
