Theorems · Theorem · number theory
Nat.mem_divisorsAntidiagonal
∀ {n : ℕ} {x : ℕ × ℕ}, x ∈ n.divisorsAntidiagonal ↔ x.1 * x.2 = n ∧ n ≠ 0- Defined in
- Mathlib.NumberTheory.Divisors
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Finset.Iccproof · cited by 348
- Ne.bot_ltproof · cited by 116
- mul_div_cancel_left₀proof · cited by 111
- Nat.divisorsAntidiagonalstatement · cited by 61
- mul_ne_zero_iffproof · cited by 39
- Finset.filterMap.congr_simpproof · cited by 1
Cited by11
Results whose statement or proof uses this declaration.
- Nat.snd_mem_divisors_of_mem_antidiagonalproof · cited by 4
- Nat.ne_zero_of_mem_divisorsAntidiagonalproof · cited by 4
- ArithmeticFunction.coe_zeta_smul_applyproof · cited by 3
- DirichletCharacter.mul_convolution_distribproof · cited by 2
- Nat.swap_mem_divisorsAntidiagonalproof · cited by 1
- Nat.divisorsAntidiagonal_eq_prod_filter_of_leproof · cited by 1
- Nat.fst_mem_divisors_of_mem_antidiagonalproof · cited by 1
- LSeries.term_convolutionproof · cited by 1
- Nat.mem_divisorsAntidiagonalListproof · cited by 0
- divisorsAntidiagonalFactors_eqproof · cited by 0
- divisorsAntidiagonalFactors_oneproof · cited by 0