Sentence examples for from proofs from inspiring English sources
Proofs of A ⊃ B are now functions from (proofs of) A to (proofs of) B and A ⊃ B itself the set of such functions.
One major advantage of Martin-Löf's formal approach to constructive mathematics is that it greatly facilitates the extraction of programs from proofs.
If quantifier-free formulae correspond to the "real" part of the mathematical theory, the first epsilon-theorem shows that ideal elements can be eliminated from proofs of real statements, provided the axioms are also real statements.
Moreover, certain forms of constructive mathematics resembles computer science in that there has to be an implementation trace: one must always be able to recover implementation information from proofs by reading between the lines.
(Actual proofs such as the ε-substitution had always been of such a kind: provide finitary procedures which eliminate transfinite elements from proofs of real statements, in particular, of 0 = 1).
The kinds of inference rules and decision procedures that one writes for proofs involving equality and rewriting are rather different from proofs that one might write in first-order logic using, say, sequent calculus or natural deduction.
Could Gene Drives go from proof of principle to UN decision in under two years?
It showed a scene from "Proof," a one-act play by Jeff Reich that was part of the Ensemble Studio Theater's "Marathon 2000" in June -- not from "Proof," the play by David Auburn that closes tomorrow at Manhattan Theater Club.
Kidnap insurance policies typically include the services of response teams that coach victims' families on everything from proof-of-life questions to ransom prices, which the policies reimburse.
Over the years the scope of the Nuprl project has expanded from "proofs-as-programs" to "systems-as-theories".
Although the field is in continuous evolution, at this moment it is moving from proofs-of-concept in simple matrices to methods dealing with matrices of higher complexity and relevant analyte concentrations.
