Sentence examples for a common proof from inspiring English sources

First we consider h(a + ) > 0. We enunciate three results and give a common proof.

Their most common "proof" of a single language is the shared use of characters in written Chinese.

"I am convinced that the impact of defendants' alleged antitrust violations cannot be shown on a class-wide basis with common proof," Judge Sippel wrote.

The 1888 piece is the most common proof coin in the series, with an official mintage of 200 pieces.

A common example of proof includes medical records that describe your emotional symptoms.

But cooperation is merely proof of a common goal - in this case the removal of white supremacy - and is not proof of a complete community of interests.

Then f and g have a common fixed point in X. Proof Repeating the proof of Theorem 4, we construct an increasing sequence { x n } in X such that x n → u for some u ∈ X.

Then, f and g have a common fixed point in X. Proof Reviewing the proof of Theorem 5, we construct an increasing sequence { x n } in X such that x n → u, for some u ∈ X.

Theorem 4 Under the hypotheses of Theorem  3, without the continuity assumption on the functions f and g, for any nondecreasing sequence { x n } in X such that x n → x ∈ X, let us have x n ⪯ x for all n ∈ N. Then f and g have a common fixed point in X. Proof Reviewing the proof of Theorem 3, we construct an increasing sequence { x n } in X such that x n → z for some z ∈ X.

The capacity to feel pain has often been put forth as proof of a common humanity.

They also must demonstrate evidence of mutual dependence such as joint financial obligations or proof of a common household.