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Theorems · Theorem · group theory

not_isOfFinAddOrder_of_injective_nsmul

∀ {G : Type u_1} [inst : AddMonoid G] {x : G}, (Function.Injective fun n => n • x) → ¬IsOfFinAddOrder x

See also injective_nsmul_iff_not_isOfFinAddOrder.

Defined in
Mathlib.GroupTheory.OrderOfElement
Cited by
2 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Quot.sound
Assumes
AddMonoid
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Around this declaration

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

AddRightCancelMonoid.injective_nsmul_iff_not_isOfFinAddOrder · cited by 1AddRightCancelMonoid.inje…injective_nsmul_iff_not_isOfFinAddOrder · cited by 1injective_nsmul_iff_not_i…AddMonoid · cited by 2864AddMonoidzero_nsmul · cited by 137zero_nsmulIsOfFinAddOrder · cited by 105IsOfFinAddOrderisOfFinAddOrder_iff_nsmul_eq_zero · cited by 27isOfFinAddOrder_iff_nsmul…irrefl · cited by 15irreflnot_isOfFinAddOrder_of_inject…CITED BYCITES

Cites5

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Cited by2

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