Nat.exists_lt_modEq_of_infinite

∀ {s : Set ℕ}, s.Infinite → ∀ {k : ℕ}, 0 < k → ∃ m ∈ s, ∃ n ∈ s, m < n ∧ m ≡ n [MOD k]

If s is an infinite set of natural numbers and k > 0, then s contains two elements m < n that are equal mod k.

Defined in: Mathlib.Combinatorics.Pigeonhole
Cited by: 1 results in Mathlib
Foundations: Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

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