Theorems · Theorem · commutative algebra
Nat.cast_comm
∀ {α : Type u_1} [inst : NonAssocSemiring α] (n : ℕ) (x : α), ↑n * x = x * ↑n- Defined in
- Mathlib.Data.Nat.Cast.Commute
- Cited by
- 16 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.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NonAssocSemiringstatement and proof · cited by 805
- Commute.eqproof · cited by 91
- Nat.cast_commuteproof · cited by 24
Cited by16
Results whose statement or proof uses this declaration.
- Commute.add_pow'proof · cited by 6
- ascPochhammer_succ_evalproof · cited by 3
- descPochhammer_eval_eq_descFactorialproof · cited by 3
- descPochhammer_succ_evalproof · cited by 3
- Commute.add_pow_prime_pow_eq'proof · cited by 3
- Odd.mulproof · cited by 3
- ascPochhammer_posproof · cited by 3
- IsUltrametricDist.isUltrametricDist_of_forall_norm_natCast_le_oneproof · cited by 1
- Polynomial.mul_X_add_natCast_compproof · cited by 1
- Polynomial.mul_X_sub_intCast_compproof · cited by 1
- Nat.cast_mul_floor_div_cancelproof · cited by 1
- Ring.descPochhammer_smeval_addproof · cited by 1