Sentence examples for this proof consists from inspiring English sources

This proof consists of three elements: 1.

Proof The proof consists of several steps.

(iii) The proof consists of two steps.

Proof The proof consists of the following steps.

end{aligned} (2.13) The proof consists of two steps.

The rest of the proof consists of several steps and claims.

Roughly, it is that mathematicians aim to prove mathematical claims of various sorts, and that proof consists of the logical derivation of a given claim from axioms.

Roughly, the method of the proof consists in deciding when the Weyl groupoid is finite, iterating the construction (2.25).

The plan for the rest of the proof consists in showing that S is (alpha_{infty} -condensing.

Again, the proof consists of two steps: Step 1: The creditor's payoff in the pure strategy equilibrium is given by begin{aligned} E[Pi ^mathrm{C}(beta _0, beta _1)] = (1 - beta _0) theta ^ + (1 - beta _1) (1 - {theta ^^2).

We prove that there exists a continuum of pairwise non (weakly) cocycle conjugate, strongly outer actions of Λ on D. The proof consists in assigning, to any second countable abelian pro-p group G, a strongly outer action of Λ on D whose (weak) cocycle conjugacy class completely remembers the group G.