Sentence examples for defined proof from inspiring English sources

Consistency is also often defined proof theoretically — Γ is (proof theoretically) consistent if there is no proof of a contradiction from Γ — but the definition above comports with the definition of a logic used in §1.1 simply as a language together with a semantics in which truth, validity, etc are definable.

There's no defined proof standard for me to use in the poster or jersey context.

This procedure has been so far confined to small research studies that can only be defined proof of concept studies often unfortunately giving conflicting results.

He defined such proof as the test flight of an Iranian missile with enough range to strike the continent.

k̃ and (T^_{k}) will be defined during proof of this theorem.

In essence, he defined a proof to be any finite sequence of statements such that each statement in the sequence either is an axiom or follows from previous members by a valid rule of inference.

Then, for every small number ε > 0, FHDE (5.1) has a solution defined on J. Proof The proof is similar to Theorem 3.1 and we omit the details.

In the proof we will use notation defined in the proof of Theorem 2.1.

Proof With Ψ and Φ defined in the proof of Theorem 3.1, it is easy to show that ∈ X × Y.

Sketch of the proof Consider two operators A, B defined in the proof of Theorem 3.1.

For convenience, we still use (theta p,X,S)) which is defined in the proof of Proposition 1, and the following proof is divided into three steps.