Sentence examples for proof includes the from inspiring English sources

The second proof includes the Lipschitz summation formula following Luo's method in [3].

The first proof includes the Cauchy residue theorem and a complex integral over a circle C following Bayad's method in [4].

There is proof, including the admissions of the perpetrator, his parents, and wife, that Josh Duggar sexually abused young girls.

Other challenges to proof include the likely time lag between infection and diagnosis, the ubiquity of many infections, the influence of age at infection, and the limitations in laboratory assays; small numbers of cases, inaccurate background leukemia rates, and difficulty tracking mobile populations further affect cluster investigations.

Tape and filler are needed around the windows for further draught-proofing, including the ones we are not replacing.

12.7 below for the proofs, including the one of Proposition 1.

This "proof" includes some of the following: wedding photos, message and email logs, and a bunch of other intrusive pieces that you might not feel comfortable sharing.

This "proof" includes some of the following: wedding photos, message and email logs, and a plethora of other intrusive pieces that you might not feel comfortable sharing.

The proof includes a construction of a word of small, sometimes minimal, weight in the dual code of any plane of square order containing a Baer subplane.

Proof includes specific quotes from the book you're writing about, or specific facts about the topic.

Now, the proof includes applying Theorem 2.10 to show that S ( x ) has an r-maximal element x ¯ ∈ S ( x ).