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Theorems · Theorem · group theory

Finset.card_pow_mono

∀ {α : Type u_2} [inst : DecidableEq α] [inst_1 : CancelMonoid α] {s : Finset α} {m n : ℕ},
  m ≠ 0 → m ≤ n → (s ^ m).card ≤ (s ^ n).card

See Finset.Nonempty.card_pow_mono for a version that works for zero powers.

Defined in
Mathlib.Algebra.Group.Pointwise.Finset.Basic
Cited by
1 results in Mathlib
Foundations
Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEqCancelMonoid
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Finset.card_le_card_pow · cited by 1Finset.card_le_card_powFinset · cited by 13712FinsetFinset.card · cited by 2327Finset.cardFinset.Nonempty · cited by 1001Finset.NonemptyFinset.eq_empty_or_nonempty · cited by 104Finset.eq_empty_or_nonemp…Finset.npow · cited by 30Finset.npowCancelMonoid · cited by 20CancelMonoidFinset.empty_pow · cited by 4Finset.empty_powFinset.Nonempty.card_pow_mono · cited by 1Nonempty.card_pow_monoFinset.card_pow_monoCITED BYCITES

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Cited by1

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