Theorems · Theorem · number theory
Finset.Nat.antidiagonal_filter_le_fst_of_le
∀ {n k : ℕ},
k ≤ n →
{a ∈ Finset.HasAntidiagonal.antidiagonal n | k ≤ a.1} =
Finset.map ({ toFun := fun x => x + k, inj' := ⋯ }.prodMap (Function.Embedding.refl ℕ))
(Finset.HasAntidiagonal.antidiagonal (n - k))- Defined in
- Mathlib.Data.Finset.NatAntidiagonal
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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 · cited by 13,712
- Finset.filterstatement · cited by 949
- Finset.mapstatement · cited by 747
- Finset.extproof · cited by 565
- Finset.HasAntidiagonal.antidiagonalstatement · cited by 218
- tsub_add_cancel_of_leproof · cited by 112
- add_right_commproof · cited by 85
- add_left_injectivestatement · cited by 49
- Function.Embedding.reflstatement and proof · cited by 29
- Function.Embedding.prodMapstatement · cited by 23
- Function.Embedding.refl_applyproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- MvPolynomial.sum_antidiagonal_card_esymm_psum_eq_zeroproof · cited by 0
- Finset.Nat.antidiagonal_filter_le_snd_of_leproof · cited by 0