[see also: follow, entail
Then x=y and y=z implies x=z. [Or: imply]
Note that M being cyclic implies F is cyclic.
However, if B were omitted in (1), the case n=0 would imply Nf=1, an undesirable restriction.
Our present assumption implies that the last inequality in (8) must actually be an equality.
That (2) implies (1) is contained in the proof of Theorem 1 of .
The continuity of f implies that of g.
The implied constants depend on r.
The equivalence of (a) and (b) is trivially implied by the definition of M.