Theorems · Theorem · dynamical systems

Dynamics.coverMincard_mul_le_pow

∀ {X : Type u_1} {T : X → X} {U : SetRel X X} {F : Set X},
  Set.MapsTo T F F →
    ∀ [U.IsSymm] (m n : ℕ), Dynamics.coverMincard T F (U.comp U) (m * n) ≤ Dynamics.coverMincard T F U m ^ n

Defined in: Mathlib.Dynamics.TopologicalEntropy.CoverEntropy
Cited by: 2 results in Mathlib
Foundations: Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: SetRel.IsSymm

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Cites27

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement and proof · cited by 53,352
Finsetproof · cited by 13,712
Top.topproof · cited by 9,680
SetLike.coeproof · cited by 8,199
ENatstatement and proof · cited by 4,985
LE.le.transproof · cited by 3,151
Set.Nonemptyproof · cited by 2,627
Finset.cardproof · cited by 2,327
MulZeroClass.mul_zeroproof · cited by 2,091
le_reflproof · cited by 2,061
eq_or_neproof · cited by 1,117
pow_zeroproof · cited by 1,094

Cited by2

Results whose statement or proof uses this declaration.

Dynamics.coverEntropyEntourage_le_log_coverMincard_divproof · cited by 2
Dynamics.coverMincard_le_powproof · cited by 0