Sentence examples for equivalence above from inspiring English sources

Yet this does not give us the inset equivalence above.

However, this renders the left to right implication in the equivalence above unsound, for it may be true that it is impermissible for me to discipline your child, but false that it is obligatory for me to see to it that your child is positively not disciplined.

We ignore most of the simple definitional equivalences mentioned above, as well as DS and TTC.

Finally, binding all equivalences above, one can easily finish the proof.

If one began with OB alone and considered the formulas on the right of the equivalences above, one could easily be led to consider them as at least candidate defining conditions for those on the left.

This correspondence, based on the equivalences above, is at the heart of the correspondence theory between modal and classical logic, which offers a systematic treatment of various aspects of temporal logic such as expressiveness, definability, and model theory with the tools and techniques of classical logic.

The rule "even × integer = even" means that the even numbers form an ideal in the ring of integers, and the above equivalence relation can be described as equivalence modulo this ideal.

This and the above equivalence imply (40).

This along with the above equivalence implies (40).

This along with the above equivalence establishes (k).

This and the above equivalence yield inequality (i).