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Proof (i) Necessity.
Proof (i) Let u ∈ E +.
Proof "(i) ⟺ (ii)" is evidence.
Proof (i) Let ⪯ = X × X.
Proof (i) Comes from Proposition 2.1 ii).
Proof (i) Suppose that u ∈ N λ +.
Proof (i) Let t = arccos ( a / b ).
Proof (i) Let ϵ > 0 be given.
Proof (i) ⇒ (ii) Suppose that (i) holds.
Proof (i) → (ii): It is obvious.
Proof (i) follows from Proposition 1.12.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com