Sentence examples for part of the proof is from inspiring English sources

Part of the proof is in all the building going on.

A crucial part of the proof is the application of an abstract uniqueness theorem, which says that such a uniqueness property follows from the existence of a jointly faithful collection of states on the ambient C⁎-algebra, each of which is the unique extension of a state on the distinguished abelian C⁎-subalgebra.

This part of the proof is tedious but unproblematic.

The first part of the proof is complete.

Thus, the first part of the proof is done.

Hence the second part of the proof is over.

Observe that the simplex S constructed in Part 1 of the proof is independent of (varepsilon>0).

The second part (2) of the proof is expressed by the following theorem: For each tested time instant t, if t is the arrival time of a mandatory instance of τ i, then Equation 5 is valid.

The main part of the proof was to compute (lambda (I^K_Omega (w))).

The crucial parts of the proof are to employ the end-point type of maximal regularity for the homogeneous heat equation and some new bilinear estimates in the Hardy space.

The remaining parts of the proof are identical with those stated above.