Sentence examples for in particular in the proof of from inspiring English sources

In particular, in the proof of the theorem, we use the f-preserving property for the barycenter of a triangle.

In particular, in the proof of the following lemma we show how the value E R ∈ Sub (S, r ) [ MPD 3 (T, R ) ] can be written analytically as an expression that contains the quantities in Table 1.

In particular, in our proof, we do not need the Lipschitz continuity of f.

In particular, a proof-of-concept prototype system that integrates these three FSs is also developed and presented.

The proof of BF in particular requires the necessitation of the formula ∀x□φ → □φ (see line 2 in the proof of the main Theorem).

The proof is analogous to Step 2 in the proof of Theorem 6 in [ 38].

It provides in particular a local proof of the dimensional functional forms of the Brunn Minkowski inequalities.

In particular, this provides a proof of the termination of Solinas algorithm.

The former Liberal Democrat leader Menzies Campbell told May that the US-UK treaty was still in need of reform, in particular the standard of proof needed.

The former Lib Dem leader Sir Menzies Campbell told May the treaty still needed reform, in particular the standard of proof required.

In particular, a proof of \(A \rightarrow B\) was no longer a construction that could be applied to any proof of \(A\) Two examples in \(\mathsf{J}\) are presented, showing modal theorems of \(\mathsf{K}\), and realizations for them.