Theorems · Theorem · commutative algebra
infinite_range_add_smul_iff
∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [IsDomain R] [Infinite R] [inst_3 : AddCommGroup M]
[inst_4 : Module R M] [Module.IsTorsionFree R M] (x y : M), (Set.range fun r => x + r • y).Infinite ↔ y ≠ 0- Defined in
- Mathlib.Algebra.Module.Torsion.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Set.rangestatement and proof · cited by 4,705
- add_zeroproof · cited by 2,707
- IsDomainstatement and proof · cited by 2,196
- smul_zeroproof · cited by 665
- Module.IsTorsionFreestatement and proof · cited by 600
- Infinitestatement and proof · cited by 352
- Set.Infinitestatement and proof · cited by 263
- add_right_injproof · cited by 71
- smul_left_injectiveproof · cited by 25
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