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feat(GroupTheory/GroupAction/Basic): additivize two lemmas (#11285)
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I see no reason for the omission of `@[to_additive]` on these two `pretransitive_iff_...` lemmas, so add it here.

From AperiodicMonotilesLean.
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jsm28 committed Mar 11, 2024
1 parent 3936b6d commit 0235206
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4 changes: 4 additions & 0 deletions Mathlib/GroupTheory/GroupAction/Basic.lean
Expand Up @@ -440,6 +440,8 @@ def orbitRel.Quotient : Type _ :=

/-- An action is pretransitive if and only if the quotient by `MulAction.orbitRel` is a
subsingleton. -/
@[to_additive "An additive action is pretransitive if and only if the quotient by
`AddAction.orbitRel` is a subsingleton."]
theorem pretransitive_iff_subsingleton_quotient :
IsPretransitive G α ↔ Subsingleton (orbitRel.Quotient G α) := by
refine ⟨fun _ ↦ ⟨fun a b ↦ ?_⟩, fun _ ↦ ⟨fun a b ↦ ?_⟩⟩
Expand All @@ -450,6 +452,8 @@ theorem pretransitive_iff_subsingleton_quotient :

/-- If `α` is non-empty, an action is pretransitive if and only if the quotient has exactly one
element. -/
@[to_additive "If `α` is non-empty, an additive action is pretransitive if and only if the
quotient has exactly one element."]
theorem pretransitive_iff_unique_quotient_of_nonempty [Nonempty α] :
IsPretransitive G α ↔ Nonempty (Unique <| orbitRel.Quotient G α) := by
rw [unique_iff_subsingleton_and_nonempty, pretransitive_iff_subsingleton_quotient, iff_self_and]
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