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Theorems · Theorem · group theory

Finset.Nonempty.card_pow_mono

∀ {α : Type u_2} [inst : DecidableEq α] [inst_1 : CancelMonoid α] {s : Finset α},
  s.Nonempty → Monotone fun n => (s ^ n).card

See Finset.card_pow_mono for a version that works for the empty set.

Defined in
Mathlib.Algebra.Group.Pointwise.Finset.Basic
Cited by
1 results in Mathlib
Foundations
Depth 83 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_pow_mono · cited by 1Finset.card_pow_monoFinset · cited by 13712FinsetFinset.card · cited by 2327Finset.cardMonotone · cited by 1397MonotoneFinset.Nonempty · cited by 1001Finset.Nonemptypow_succ · cited by 374pow_succmonotone_nat_of_le_succ · cited by 45monotone_nat_of_le_succFinset.npow · cited by 30Finset.npowCancelMonoid · cited by 20CancelMonoidFinset.card_le_card_mul_right · cited by 3Finset.card_le_card_mul_r…Nonempty.card_pow_monoCITED BYCITES

Cites9

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Cited by1

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