Sentence examples for fundamental proof from inspiring English sources

Although one hybrid line showed phenotypic instability, our results provide a fundamental proof of principle, demonstrating that apomixis can indeed be used in plant breeding and seed production to fix complex, quantitative phenotypes across generations.

They will also believe it in the face of irrefutable counter-evidence and millennia of fundamental proof.

Indeed, the enduring popularity of the argument from miracles underscores the truth of Butler's observation that miracles are one of the "direct and fundamental proofs" of Christianity.

The following lemma is fundamental in proofs of our main results.

The parallel postulate is fundamental for the proof of the theorem that the sum of the angles of a triangle is always 180 degrees.

The following fixed-point theorem is fundamental for the proof of the best approximation theorem.

The following lemmas are fundamental in the proof of our main results of this section.

The following Schaefer's fixed-point theorem is fundamental in the proof of our main results.

In the following, we present the useful lemmas which are fundamental in the proof of our main results.

Here it suffices to recall that a fundamental theme of proof theory (and in particular that part of it which is known as ordinal analysis) is the classification of theories by means of transfinite ordinals that measure their "consistency strength" and "computational power".

The neo-scholastic and neo-Thomist traditions, which also reject the ontological argument (as did Thomas Aquinas), do not accept Kant's account that makes the ontological proof fundamental to other arguments (e.g., cosmological, teleological) that Aquinas formulated to demonstrate that there is a God.