Theorems · Theorem · commutative algebra
Nat.cast_one
∀ {R : Type u_1} [inst : AddMonoidWithOne R], ↑1 = 1- Defined in
- Mathlib.Data.Nat.Cast.Defs
- Cited by
- 2,501 results in Mathlib
- Foundations
- Depth 10 from the axioms, rests on 48 definitions · uses no axioms
- Assumes
- AddMonoidWithOne
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.
- zero_addproof · cited by 2,366
- Nat.cast_zeroproof · cited by 1,870
- AddMonoidWithOnestatement and proof · cited by 313
- Nat.cast_succproof · cited by 99
Cited by2,501
Results whose statement or proof uses this declaration.
- Int.cast_oneproof · cited by 371
- Nat.cast_mulproof · cited by 309
- Int.cast_negproof · cited by 224
- Nat.cast_pos'proof · cited by 219
- Int.cast_mulproof · cited by 113
- Rat.cast_intCastproof · cited by 74
- one_add_one_eq_twoproof · cited by 65
- Complex.exp_zeroproof · cited by 43
- Ordinal.one_lt_omega0proof · cited by 39
- Cardinal.lift_natCastproof · cited by 39
- ENNReal.mul_inv_cancelproof · cited by 37
- Polynomial.derivative_Xproof · cited by 34
Showing the 200 most cited of 2,501.