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Theorems · Theorem · group theory

Set.finite_add

∀ {α : Type u_2} [inst : Add α] [IsLeftCancelAdd α] [IsRightCancelAdd α] {s t : Set α},
  (s + t).Finite ↔ s.Finite ∧ t.Finite ∨ s = ∅ ∨ t = ∅
Defined in
Mathlib.Algebra.Group.Pointwise.Set.Finite
Cited by
1 results in Mathlib
Foundations
Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddIsLeftCancelAddIsRightCancelAdd
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.natCard_add_le · cited by 1Set.natCard_add_leSet · cited by 53352SetSet.Finite · cited by 1814Set.FiniteSet.add · cited by 338Set.addFunction.Injective.injOn · cited by 280Injective.injOnIsLeftCancelAdd · cited by 72IsLeftCancelAddIsRightCancelAdd · cited by 69IsRightCancelAddadd_left_injective · cited by 49add_left_injectiveadd_right_injective · cited by 36add_right_injectiveSet.finite_image2 · cited by 4Set.finite_image2Set.finite_addCITED BYCITES

Cites9

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Cited by1

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