Theorems · Theorem · group theory
zmultiples_equiv_zmultiples_apply
∀ {G : Type u_1} [inst : AddGroup G] {x y : G} [inst_1 : Finite G] (h : addOrderOf x = addOrderOf y) (n : ℕ),
(zmultiplesEquivZMultiples h) ⟨n • x, ⋯⟩ = ⟨n • y, ⋯⟩- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Equivstatement and proof · cited by 8,337
- AddGroupstatement and proof · cited by 4,410
- Equiv.symmproof · cited by 3,681
- AddSubgroupstatement · cited by 3,232
- Finitestatement and proof · cited by 3,029
- AddSubgroup.zmultiplesstatement and proof · cited by 493
- Equiv.transproof · cited by 337
- addOrderOfstatement and proof · cited by 208
- natCast_zsmulstatement and proof · cited by 118
- Equiv.eq_symm_applyproof · cited by 85
- finCongrproof · cited by 78
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