Theorems · Theorem · number theory
Nat.frequently_modEq
∀ {n : ℕ}, n ≠ 0 → ∀ (d : ℕ), ∃ᶠ (m : ℕ) in Filter.atTop, m ≡ d [MOD n]Infinitely many natural numbers are equal to d mod n.
- Defined in
- Mathlib.Order.Filter.AtTopBot.ModEq
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filter.atTopstatement · cited by 2,405
- Nat.cast_addproof · cited by 586
- Filter.Tendsto.compproof · cited by 560
- Filter.Frequentlystatement · cited by 414
- nsmul_eq_mulproof · cited by 369
- Nat.cast_mulproof · cited by 309
- Nat.ModEqstatement and proof · cited by 225
- Filter.tendsto_idproof · cited by 180
- Ne.bot_ltproof · cited by 116
- Filter.Frequently.of_forallproof · cited by 25
- Filter.tendsto_add_atTop_natproof · cited by 19
- sub_add_cancel_rightproof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- Nat.frequently_mod_eqproof · cited by 2