Theorems · Theorem · commutative algebra
Nat.commute_cast
∀ {α : Type u_1} [inst : NonAssocSemiring α] (x : α) (n : ℕ), Commute x ↑n- Defined in
- Mathlib.Data.Nat.Cast.Commute
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
- Assumes
- NonAssocSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NonAssocSemiringstatement and proof · cited by 805
- Commutestatement · cited by 639
- Commute.symmproof · cited by 79
- Nat.cast_commuteproof · cited by 24
Cited by13
Results whose statement or proof uses this declaration.
- Rat.cast_divInt_of_ne_zeroproof · cited by 5
- NNRat.cast_divNat_of_ne_zeroproof · cited by 4
- Rat.cast_add_of_ne_zeroproof · cited by 2
- Set.natCast_mem_centerproof · cited by 2
- Rat.cast_mul_of_ne_zeroproof · cited by 1
- Commute.ofNat_rightproof · cited by 1
- NNRat.cast_mul_of_ne_zeroproof · cited by 1
- NNRat.cast_add_of_ne_zeroproof · cited by 1
- SemiconjBy.natCast_mul_rightproof · cited by 1
- Finset.sum_pow_eq_sum_piAntidiag_of_commuteproof · cited by 1
- Rat.cast_div_of_ne_zeroproof · cited by 0
- NNRat.cast_div_of_ne_zeroproof · cited by 0