Theorems · Theorem · combinatorics
Finset.card_add_card_subsetSum_lt_card_subsetSum_insert_max
∀ {M : Type u_1} [inst : DecidableEq M] [inst_1 : AddCommMonoid M] {A : Finset M} {a : M} [inst_2 : LinearOrder M]
[IsOrderedCancelAddMonoid M],
(∀ x ∈ A, 0 < x) → (∀ x ∈ A, x < a) → 0 < a → A.card + A.subsetSum.card < (insert a A).subsetSum.card- Defined in
- Mathlib.Combinatorics.Additive.SubsetSum
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
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
- AddCommMonoidstatement and proof · cited by 12,281
- LinearOrderstatement and proof · cited by 8,572
- SetLike.coeproof · cited by 8,199
- Finset.cardstatement and proof · cited by 2,327
- Disjointproof · cited by 2,201
- LT.lt.leproof · cited by 2,189
- le_reflproof · cited by 2,061
- HVAdd.hVAddproof · cited by 1,820
- LT.lt.ne'proof · cited by 1,417
- le_imp_le_of_le_of_leproof · cited by 576
- IsOrderedCancelAddMonoidstatement and proof · cited by 359
Cited by1
Results whose statement or proof uses this declaration.
- Finset.card_succ_choose_two_lt_card_subsetSum_of_posproof · cited by 1