Theorems · Theorem · group theory
Set.infinite_mul
∀ {α : Type u_2} [inst : Mul α] [IsLeftCancelMul α] [IsRightCancelMul α] {s t : Set α},
(s * t).Infinite ↔ s.Infinite ∧ t.Nonempty ∨ t.Infinite ∧ s.Nonempty- Cited by
- 0 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Nonemptystatement · cited by 2,627
- Set.mulstatement · cited by 297
- Function.Injective.injOnproof · cited by 280
- Set.Infinitestatement · cited by 263
- IsLeftCancelMulstatement and proof · cited by 51
- IsRightCancelMulstatement and proof · cited by 43
- mul_left_injectiveproof · cited by 19
- mul_right_injectiveproof · cited by 15
- Set.infinite_image2proof · cited by 5
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