Sentence examples for proof of formula from inspiring English sources

Proof Proof of formula (10) follows now immediately from (7). □.

Formula (1.9.2) can be proved by analogy with the proof of formula (1.2.1) for functions of self-adjoint operators.

Proof See Banyaga [4] ; Wang [57] gives an elementary proof of formula (11).

□ See Banyaga [4]; Wang [57] gives an elementary proof of formula (11).

AI designed the algorithm and performed the mathemathical proof of formula.

Our proof of formula (6) related to the ROC straight line graph corresponds to Bamber's OD curve related proof.

Archimedes' proofs of formulas for areas and volumes set the standard for the rigorous treatment of limits until modern times.

In FL, proofs of formulas like ∃x□(x=t), ∀y□ ∃x(x=y), (CBF), and (BF), which seem incompatible with the world-relative interpretation, are blocked.

In the formulas-as-types analogy which is so popular and fruitful in theoretical computer science, a logical system is put in correspondence with a typed computational device (like typed lambda calculus), by associating to each proof of a formula a program having as type that very formula.

Rosser's generalization involves applying the fixed point theorem to the formula R x): 'for all z: either z is not the Gödel number of a proof of the formula with Gödel number x or there is a proof shorter than z of the negation of (the formula with Gödel number) x' (see Rosser 1936).

Hence we come to the final steps of our proof of the formula for I t), the first of which is to derive explicit formulas for the radial parts of the Laplace-Casimir operators (D(I_ell )).