Theorems · Theorem · combinatorics

Finset.mem_piAntidiag

∀ {ι : Type u_1} {μ : Type u_2} [inst : DecidableEq ι] [inst_1 : AddCommMonoid μ] [inst_2 : Finset.HasAntidiagonal μ]
  [inst_3 : DecidableEq μ] {s : Finset ι} {n : μ} {f : ι → μ},
  f ∈ s.piAntidiag n ↔ s.sum f = n ∧ ∀ (i : ι), f i ≠ 0 → i ∈ s

Defined in: Mathlib.Algebra.Order.Antidiag.Pi
Cited by: 1 results in Mathlib
Foundations: Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: DecidableEq AddCommMonoid Finset.HasAntidiagonal DecidableEq

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Cites17

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

DFunLike.coeproof · cited by 62,936
Finsetstatement and proof · cited by 13,712
AddCommMonoidstatement and proof · cited by 12,281
Equivproof · cited by 8,337
Finset.sumstatement and proof · cited by 5,195
Equiv.symmproof · cited by 3,681
Finset.univproof · cited by 3,473
Finset.cardproof · cited by 2,327
Subtype.coe_etaproof · cited by 110
Fintype.card_coeproof · cited by 72
Finset.sum_attachproof · cited by 54
Finset.HasAntidiagonalstatement and proof · cited by 48

Cited by1

Results whose statement or proof uses this declaration.

Finset.sum_pow_eq_sum_piAntidiag_of_commuteproof · cited by 1