Sentence examples for proof 1 from inspiring English sources
Proof (1) Since r p k > 1 and ∑ k s 1 p k = r, we get ∑ k s 1 r p k = 1.
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Proof (1) and (2) are immediate.
Proof (1∘) We first prove that { x n } n = 0 ∞ is bounded.
Proof (1 - 2) Proceeding as in the proof of Theorem 4, the parts (1) and (2) hold.
The original Branciari's proof [1] deals with one-dimensional integral, and such conclusion is valid due to the implication (3.1).
Proof 1° It follows from gx0 ≼ fx0 = gx1 that fx0 ≼ fx1, i.e., y0 ≼ y1 and it is easy to proceed by induction.
Diagrams are usually adopted as a heuristic tool in exploring a proof, but not as part of a proof.[1] It is a quite recent movement among philosophers, logicians, cognitive scientists and computer scientists to focus on different types of representation systems, and much research has been focussed on diagrammatic representation systems in particular.
