Theorems · Theorem · combinatorics
Finset.mem_finsuppAntidiag_insert
∀ {ι : Type u_1} {μ : Type u_2} [inst : DecidableEq ι] [inst_1 : AddCommMonoid μ] [inst_2 : Finset.HasAntidiagonal μ]
[inst_3 : DecidableEq μ] {a : ι} {s : Finset ι},
a ∉ s →
∀ (n : μ) {f : ι →₀ μ},
f ∈ (insert a s).finsuppAntidiag n ↔
∃ m ∈ Finset.HasAntidiagonal.antidiagonal n, ∃ g, f = g.update a m.1 ∧ g ∈ s.finsuppAntidiag m.2- Defined in
- Mathlib.Algebra.Order.Antidiag.Finsupp
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- Finsuppstatement and proof · cited by 5,255
- Finset.sumproof · cited by 5,195
- LE.le.transproof · cited by 3,151
- Finset.sum_congrproof · cited by 2,323
- Finsupp.supportproof · cited by 828
- Finset.HasAntidiagonal.antidiagonalstatement · cited by 218
- Function.update_selfproof · cited by 201
- Function.update_of_neproof · cited by 198
- Finset.sum_insertproof · cited by 196
Cited by1
Results whose statement or proof uses this declaration.
- Finset.finsuppAntidiag_insertproof · cited by 1