Theorems · Theorem · commutative algebra
Nat.cast_add
∀ {R : Type u_1} [inst : AddMonoidWithOne R] (m n : ℕ), ↑(m + n) = ↑m + ↑n- Defined in
- Mathlib.Data.Nat.Cast.Defs
- Cited by
- 586 results in Mathlib
- Foundations
- Depth 10 from the axioms, rests on 51 definitions · uses propext
- Assumes
- AddMonoidWithOne
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- add_zeroproof · cited by 2,707
- Nat.cast_zeroproof · cited by 1,870
- add_assocproof · cited by 746
- AddMonoidWithOnestatement and proof · cited by 313
- Nat.cast_succproof · cited by 99
Cited by587
Results whose statement or proof uses this declaration.
- Nat.cast_mulproof · cited by 309
- Int.cast_negproof · cited by 224
- Nat.cast_pos'proof · cited by 219
- Int.cast_addproof · cited by 124
- Int.cast_mulproof · cited by 113
- one_add_one_eq_twoproof · cited by 65
- Nat.cast_subproof · cited by 54
- Cardinal.lift_natCastproof · cited by 39
- Polynomial.derivative_mulproof · cited by 35
- Real.log_powproof · cited by 29
- Int.cast_smul_eq_zsmulproof · cited by 28
- zsmul_oneproof · cited by 26
Showing the 200 most cited of 587.