Sentence examples for combined proof from inspiring English sources

The Drapier agreed with the Irish interpretation of the law and incorporated aspects of Molyneux's arguments that combined proof the law was misinterpreted and Locke's political philosophy.

The remaining part of the proof is similar to that of Theorem 3.3 (a combined proof of Theorems 3.1 and 3.2) and is therefore omitted.

Inspired by proof planning critics, the technique combines proof-failure analysis with modelling heuristics.

Proof Combining the proof of Lemma 3.1 with Lemma 3.2, we can obtain the conclusion.

Proof of Theorem 2.3: Combining the proof of (4.2) with the assumptions of (H5 - H7) and g(x) satisfying a local Lipschitz condition around the point x, we can get that E g n ( x ) - g ( x ) = O n - 1 / 4. (4.5).

Combined, the proofs of the downward and upward Löwenheim-Skolem theorems show that for any satisfiable set Γ of sentences, if there is no finite bound on the models of Γ, then for any infinite cardinal κ, there is a model of Γ whose domain has size exactly κ.

Proof It can be proved by combining the proof method of Theorem 3.5 and Lemma 3.3 iv).

Combining the proof of (i) and (ii), we complete this proof.

Combining the proof of (i) and (ii), we complete the proof of Theorem 3.1.

Hence, combining the proof of Case 1 and Case 2, the proof is completed.

It is found that the deviation acceleration is almost independent of the shape of proof mass for the combined configuration of proof mass with outer reference mass in ASTROD mission, while it depends on the dimensions of outer reference mass.