Theorems · Theorem · combinatorics
Finset.HasAntidiagonal.mem_antidiagonal
∀ {A : Type u_1} {inst : AddMonoid A} [self : Finset.HasAntidiagonal A] {n : A} {a : A × A},
a ∈ Finset.HasAntidiagonal.antidiagonal n ↔ a.1 + a.2 = nA pair belongs to antidiagonal n iff the sum of its components is equal to n.
- Defined in
- Mathlib.Algebra.Order.Antidiag.Prod
- Cited by
- 51 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finset.HasAntidiagonal
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- AddMonoidstatement and proof · cited by 2,864
- Finset.HasAntidiagonal.antidiagonalstatement · cited by 218
- Finset.HasAntidiagonalstatement and proof · cited by 48
Cited by51
Results whose statement or proof uses this declaration.
- Polynomial.coeff_mulproof · cited by 29
- MvPolynomial.coeff_mulproof · cited by 10
- Finset.HasAntidiagonal.antidiagonal_zeroproof · cited by 8
- PowerSeries.coeff_X_pow_mul'proof · cited by 7
- Finset.HasAntidiagonal.antidiagonal.fst_leproof · cited by 6
- PowerSeries.le_order_mulproof · cited by 5
- Polynomial.coeff_mul_X_pow'proof · cited by 5
- Polynomial.coeff_mul_degree_add_degreeproof · cited by 5
- MvPowerSeries.mul_invOfUnitproof · cited by 4
- Finset.HasAntidiagonal.antidiagonal_congrproof · cited by 4
- NormedSpace.exp_add_of_commute_of_mem_ballproof · cited by 3
- Finset.HasAntidiagonal.antidiagonal.snd_leproof · cited by 3