Sentence examples for structure of the proof from inspiring English sources

Starting from this system, the structure of the proof of Theorem 3.1 remains unchanged.

With this linear expression, the structure of the proof of Theorem 3.1 remains unchanged.

Despite the discrete setting, the structure of the proof is close to Hopf's approach to the classical Lefschetz theorem [10].

As the s constant inserted in Equation 3 does not change the structure of the proof in[17], it will not be repeated here.

Intuitively, y is a concrete analogue of the abstract notion of a construction constituting the meaning of F. The proof is by induction on the structure of the proof of F in intuitionistic first order arithmetic.

In what concerns part (1), the structure of the proof is similar to the one presented in[17] considering the existence of s pattern spins in the (m,k -firm specification.

For completeness and self-contained structure of the proofs of Theorems 1.1 and 1.2, we need the following result of [13].

And various physical theories can be objectively compared with respect to the structure of the proofs they contain.

The structure of this proof is as follows.

If one looks at an arrow A → B in a category as a kind of abstract proof of B from A, we have a representation which goes beyond pure derivability of B from A (as the arrow has its individuality), but does not deal with the particular syntactic structure of this proof.

Section  4 analyzes the structure of the locally strategy proof planning procedures.