Sentence examples for proof constructed from inspiring English sources

By virtue of this, the proof constructed by SNARK in the process of proving a given conjecture forms an explicit trace or "explanation", including the specific axioms used, and the ways in which the variables were bound in the axioms that lead to a given result; the more explicit the subject domain theory, the more detailed the explanation.

Moreover, z ∈ ⋂ i = 1 m A i. Proof Construct the complete metric space ( X, p ) of Proposition 1, and observe that from the well-known fact that for a i ∈ R +, i = 1, …, k, one has ϕ ( max i a i ) = max i ϕ ( a i ), one has M p ( x, y ) = φ ( M d ( x, y ) ). for all x, y ∈ X.

As in LK, proofs constructed in NK are represented as trees with the proof's conclusion sitting at the root of the tree, and the problem's assumptions sitting at the leaves.

In case of the negative representation one assumes that a formula corresponding to a matrix is unsatisfiable and proofs constructed for this representation are indirect.

Proof Construct a sequence { x n } as in the proof of Theorem 6.

The proof is constructed in several steps.

The Proof is constructed for durable polyurethane coated with a thick silicone wrapping.

The proof is constructed from the next three lemmas.

"Stampede has been used for everything from determining earthquake risks to help set building codes for homes and commercial buildings, to computing the largest mathematical proof ever constructed".

In this proof, SHUNYATA constructed several closed formulas on the basis of elementary rules for the formation of formulas and proved that one of these formulas is undecidable.

In the proof we constructed, for sufficiently large N, a suitable updating function f for Boolean systems B = ( 2 N, f ) such that f was cooperative, bi-quadratic, and worked as required.