Sentence examples similar to equivalent the above from inspiring English sources

Since each of φ1 and φ2 fixes an n-ary truth-function of the variables involved, and these truth-functions are distinct (since φ1 and φ2 were to be non-equivalent) the above Vf / Vg application of Rautenberg's result tells us that neither of ⊢1, ⊢2, is included in the other.

The problem of the removal of halftone dots is the two-dimensional equivalent of the above process.

This operation is equivalent to the above strategy plus a lengthening of the maturity of the Treasury's outstanding debt, something the Treasury can accomplish or avoid without help from the Fed.As a background, the Fed has, since August 2008, expanded its balance sheet by around $1 trillion.

The exchangeability condition is equivalent to the above symmetry condition.

The authors proved that the Cauchy equation is equivalent to the above equation.

They proved that the Cauchy equation is equivalent to the above equation.

First, we will give the conditions which are equivalent to the above mentioned definitions.

It is usually claimed that this view is equivalent to the above "self-ownership" version of libertarianism.

This readily implies that (1) and (46) are equivalent under the above conditions on a, b, q, s,  and (gamma ).

Kim initially maintained that the modal operator versions are equivalent to the above possible world definitions of weak and strong supervenience respectively (see esp. 1987, 79 82).

Although Ludwig's meta-theoretical framework is slightly different, the first part of his solution is essentially equivalent to the above one.