Conjectura
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Arithmetic progression

ContainsAPOfLengthdef

A set of naturals contains an arithmetic progression of length k when some a and positive common difference d place all of a, a+d, …, a+(k-1)d inside it.

def ContainsAPOfLength (S : Set ℕ) (k : ℕ) : Prop :=
  ∃ a d : ℕ, 0 < d ∧ ∀ i < k, a + i * d ∈ S

import Conjectura.Defs.Mathematics.Combinatorics.ArithmeticProgression · maintainer — open · raw source

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