Sentence examples for proof for a given from inspiring English sources

Classical automated theorem proving of today is based on ingenious search techniques to find a proof for a given theorem in very large search spaces often in the range of several billion clauses.

Proof For a given sequence x = ( x k ) ∈ c λ ( G m ), we assume that conditions (4.1 - 4.5 4.1 - 4.5

Proof For a given non-negative random variable τ and a constant c > 0, we define τ ( c ) : = { τ, if  τ ≤ c, 0, otherwise.

Lemma 3.4 If hypothesis (F4) holds, then J ∣ W 0 ≥ - ∞. Proof: For a given 0 < ε < m 0 p - 1, we can find C ε > 0 such that F ( x, u ) ≤ ε p η ∣ u ∣ p + C ε for a.e.

While this in no way constitutes a mathematical proof for any given system, the underlying behavior is common and intuitively understandable.

Because animal modeling systems are required to provide proof of efficacy for a given intervention, these regulations have commonly been referred to as "The Animal Rule" [ 298].

Similar to the proof of Theorem 2.1 for a given with, let denote the largest integer such that.

Proof: The increment/decrement factor for a given positive/negative interaction is calculated by using Equations 3 and 4 respectively.

Given K, ρ K, L) is an increasing function of L. Proof: We shall prove, for a given K, ρ K, L) is an increasing function of L by showing that ρ K, L + 1)/ρ K, L) ≥ 1.

Note that, due to a high condition number γ 1 of the B-Spline basis (see proof of Lemma 1), for a given mesh size a higher polynomial order adversely affects the condition number of the matrix A ¯ h, see [24].

Intuitively, if soundness and completeness have been established for a particular proof system and a given model-centered account of consequence, then the two accounts agree with each other: there is a proof of an argument if and only if there is no counterexample to it.