Sentence examples for the proofs contained from inspiring English sources

Axioms are simply the assumptions of the proofs contained in the physical theory.

The remaining part of the proof contains three steps.

This part of the proof contains a lot of technical details and is very difficult to follow.

A dynamic proof for an adaptive logic of inductive generalizations may look as follows: The last column of each line of the proof contains its condition, i.e., a set of abnormalities Υ that encodes the assumptions used to derive the formula in the second column of the line: each υ ∈ Υ is assumed to be false.

Fallis claims that such gaps are not unusual and that at least some of the time proofs containing them are accepted by mathematicians in a justificatory context.

The initial proof, contained in [50], is valid for Alexandroff spaces.21 The generalization of the same result to arbitrary MMS satisfying (CD K,infty )) is done in [6].

The main results complement some recent ones in the literature, while their proofs contain some refined methodological details.

It is worth pointing out that our proofs contain some new techniques.

Appendix B: Supporting lemmas and proofs contains all proofs.

This article unifies preliminary work by the authors[40, 41], presents previously unpublished aspects of the proofs, and contains updated experimental results.

And various physical theories can be objectively compared with respect to the structure of the proofs they contain.