Theorems · Theorem · number theory

threeGPFree_insert

∀ {α : Type u_2} [inst : CommMonoid α] [IsCancelMul α] {s : Set α} {a : α},
  ThreeGPFree (insert a s) ↔
    ThreeGPFree s ∧
      (∀ ⦃b : α⦄, b ∈ s → ∀ ⦃c : α⦄, c ∈ s → a * c = b * b → a = b) ∧
        ∀ ⦃b : α⦄, b ∈ s → ∀ ⦃c : α⦄, c ∈ s → b * c = a * a → b = a

Defined in

Mathlib.Combinatorics.Additive.AP.Three.Defs

Cited by

1 results in Mathlib

Foundations

Depth 8 from the axioms · uses propext

Assumes

CommMonoidIsCancelMul