Theorems · Theorem · group theory
Finset.card_le_card_add_self
∀ {α : Type u_2} [inst : Add α] [IsLeftCancelAdd α] [inst_2 : DecidableEq α] {s : Finset α}, s.card ≤ (s + s).cardThe size of s + s is at least the size of s, version with left-cancellative addition.
See card_le_card_add_self' for the version with right-cancellative addition.
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- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Finset.cardstatement and proof · cited by 2,327
- Finset.Nonemptyproof · cited by 1,001
- Finset.addstatement · cited by 133
- Finset.eq_empty_or_nonemptyproof · cited by 104
- IsLeftCancelAddstatement and proof · cited by 72
- Finset.add_emptyproof · cited by 5
- Finset.card_le_card_add_leftproof · cited by 4
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