English
For monic p ∈ F[X] that splits via f: F →* K, with B bounding the roots of map f p, then for each i the i-th coefficient satisfies ∥(map f p).coeff i∥ ≤ max{B,1}^{deg p} · deg p choose i.
Русский
Для моноичного p ∈ F[X], что распадается через f: F →* K, и если корни map f p ограничены B, то для каждого i выполняется ∥coeff i∥ ≤ max(B,1)^{deg p} · deg p choose i.
LaTeX
$$$\\forall i,\\; \\| (map f p).coeff i \\| ≤ \\max(B,1)^{p. natDegree} \\binom{p. natDegree}{i}$$$
Lean4
/-- If a group acts properly then in particular it acts continuously. -/
@[to_additive /-- If a group acts properly then in particular it acts continuously. -/
]
-- See note [lower instance property]
instance (priority := 100) toContinuousSMul [ProperSMul G X] : ContinuousSMul G X where
continuous_smul := isProperMap_smul_pair.continuous.fst
