Theorems · Theorem · group theory
npow_one
∀ {M : Type u_1} [inst : MulOneClass M] [inst_1 : Pow M ℕ] [NatPowAssoc M] (x : M), x ^ 1 = x- Defined in
- Mathlib.Algebra.Group.NatPowAssoc
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- MulOneClassPowNatPowAssoc
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MulOneClassstatement and proof · cited by 1,018
- NatPowAssocstatement and proof · cited by 53
- NatPowAssoc.npow_oneproof · cited by 1
Cited by15
Results whose statement or proof uses this declaration.
- Ring.descPochhammer_eq_factorial_smul_chooseproof · cited by 8
- Polynomial.descPochhammer_smeval_eq_ascPochhammerproof · cited by 2
- Polynomial.smeval_mul_Xproof · cited by 2
- Polynomial.ascPochhammer_smeval_neg_eq_descPochhammerproof · cited by 1
- Nat.cast_npowproof · cited by 1
- npow_mulproof · cited by 1
- Polynomial.descPochhammer_smeval_eq_descFactorialproof · cited by 1
- Ring.descPochhammer_succ_succ_smevalproof · cited by 1
- Polynomial.smeval_X_mulproof · cited by 1
- Ring.ascPochhammer_succ_succproof · cited by 1
- Ring.choose_smul_chooseproof · cited by 1
- Polynomial.smeval_at_zeroproof · cited by 0