Theorems · Theorem · group theory
pow_eq_pow_iff_modEq
∀ {G : Type u_1} [inst : LeftCancelMonoid G] {x : G} {m n : ℕ}, x ^ n = x ^ m ↔ n ≡ m [MOD orderOf x]- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LeftCancelMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- orderOfstatement and proof · cited by 324
- pow_addproof · cited by 315
- Nat.ModEqstatement and proof · cited by 225
- le_of_not_geproof · cited by 72
- LeftCancelMonoidstatement and proof · cited by 28
- Nat.ModEq.commproof · cited by 11
- Nat.ModEq.add_left_cancel'proof · cited by 7
- Nat.ModEq.add_leftproof · cited by 6
- mul_left_cancel_iffproof · cited by 6
- pow_eq_one_iff_modEqproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.autToPow_specproof · cited by 5
- IsCyclic.extproof · cited by 1
- pow_inj_modproof · cited by 1
- injective_pow_iff_not_isOfFinOrderproof · cited by 1
- pow_inj_iff_of_orderOf_eq_zeroproof · cited by 0