Theorems · Theorem · commutative algebra
Nat.cast_commute
∀ {α : Type u_1} [inst : NonAssocSemiring α] (n : ℕ) (x : α), Commute (↑n) x- Defined in
- Mathlib.Data.Nat.Cast.Commute
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext
- Assumes
- NonAssocSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.cast_zeroproof · cited by 1,870
- NonAssocSemiringstatement and proof · cited by 805
- Commutestatement and proof · cited by 639
- Nat.cast_succproof · cited by 99
- Commute.one_leftproof · cited by 15
- Commute.add_leftproof · cited by 9
- Commute.zero_leftproof · cited by 6
Cited by24
Results whose statement or proof uses this declaration.
- Polynomial.derivative_mulproof · cited by 35
- Nat.cast_commproof · cited by 16
- Nat.commute_castproof · cited by 13
- Int.cast_commuteproof · cited by 7
- Rat.cast_injectiveproof · cited by 5
- Polynomial.taylor_coeffproof · cited by 4
- IsNilpotent.exp_add_of_commuteproof · cited by 3
- IsUnit.natCast_factorial_of_leproof · cited by 2
- NNRat.cast_commuteproof · cited by 2
- Rat.cast_add_of_ne_zeroproof · cited by 2
- Rat.cast_commuteproof · cited by 2
- ArithmeticFunction.coe_zeta_mul_commproof · cited by 2