Sentence examples for modification of proposition from inspiring English sources
The following is a modification of Proposition 2.6 in [12].
(III) A modification of Proposition 4.2 is given in [12] and applied to similar problems.
A simple modification of Proposition 1 reveals that our model is canonical except for permutation.
The following criterion for compactness follows from an easy modification of [[25], Proposition 3.11].
Maietti's modification of the propositions-as-types doctrine to bring it into line with the set-theoretic interpretation of formulas is, in essence, to take propositions (or formulas) to correspond to mono-objects, that is, singletons, rather than to arbitrary sets.
Moreover, the modification of the proof of Proposition 3.1 in [4] shows that the operators (Psi^{prime}, H^{prime}:Xto X^) are compact.
A slight modification of the proof of Proposition 2.6 of Arcoya and Ruiz [15] in order to accommodate the presence of the extra linear term − Δ u leads to the following strong comparison principle.
Step 2. By (2.11) and a slight modification of the proof of [3, Proposition 3.4], we can prove that (mathcal{G}:mathbb{B} tomathbb{B}) is continuous and (mathcal{G}(mathbb{B})subsetmathbb{B}) is precompact in (mathbf {L}^{3}(0,T)).
A. Proof of Proposition 1.
The Proof of Proposition 3.6.
