Theorems · Theorem · commutative algebra
infinite_range_add_nsmul_iff
∀ {M : Type u_2} [inst : AddCommGroup M] [IsAddTorsionFree M] (x y : M), (Set.range fun n => x + n • 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
- Assumes
- AddCommGroupIsAddTorsionFree
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- Set.rangestatement and proof · cited by 4,705
- add_zeroproof · cited by 2,707
- Set.Infinitestatement and proof · cited by 263
- IsAddTorsionFreestatement and proof · cited by 155
- natCast_zsmulproof · cited by 118
- nsmul_zeroproof · cited by 73
- add_right_injproof · cited by 71
- smul_left_injectiveproof · cited by 25
- Set.range_constproof · cited by 25
- Set.infinite_range_of_injectiveproof · cited by 9
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