Sentence examples for start of the proof from inspiring English sources

Before the start of the proof, consider such a lemma which will be used to assist the convex transformation of constraint C1.2.1.

But γ < 1 violates the lower bound on γ given at the start of the proof.

The proof that the two inequalities at the start of the proof also imply (h, l | h ) ≻ (l, l | h ) is again by contradiction.

But then C h − C l ⩾ γ [ E β a (π c ) + P l ] = γ [ E β a (π c ) − V + P h ] + γ (V − P h + P l ) ⩾ P h − P l + γ (V − P h + P l ), where the last inequality follows from the lower bound on γ mentioned at the start of the proof.

Then P h − C l − γ max { E β a (π c ) + P h, 0 } > P l − C l − γ max { E β a (π c ) + P l, 0 } ⇔ P h − P l > γ (P h − P l ), where the ⇔ follows from the lower bound on E (π c ) given at the start of the proof (which implies that the max operator selects the first term in on both sides of the inequality).

As we said above the starting point of the proof is the Fuglede estimate for nearly spherical sets.

Now we start the preparation of the proof of Theorem 1.1.

Proof of Theorem 5.2 Let us start with the proof of the assertion (1).

We start with the proof of the unicity of tangent line passing through a certain point (0,B 0,B

Despite 12 months of exhaustive investigations in France and Britain, "there is not the start of the beginning of proof" of who may have been responsible, Mr Maillaud said.

We start with the proof of the following auxiliary lemma.