Theorems · Theorem · commutative algebra
Nat.cast_mul
∀ {α : Type u_1} [inst : NonAssocSemiring α] (m n : ℕ), ↑(m * n) = ↑m * ↑n- Defined in
- Mathlib.Data.Nat.Cast.Basic
- Cited by
- 309 results in Mathlib
- Foundations
- Depth 18 from the axioms, rests on 153 definitions · 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.
- mul_oneproof · cited by 3,885
- Nat.cast_oneproof · cited by 2,501
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.cast_zeroproof · cited by 1,870
- NonAssocSemiringstatement and proof · cited by 805
- Nat.cast_addproof · cited by 586
- mul_addproof · cited by 413
Cited by310
Results whose statement or proof uses this declaration.
- Complex.exp_addproof · cited by 55
- NormedSpace.expSeries_radius_eq_topproof · cited by 27
- Nat.castRingHomproof · cited by 27
- CharP.existsproof · cited by 16
- Nat.cast_divproof · cited by 8
- ZMod.unitsMap_surjectiveproof · cited by 7
- Field.finSepDegree_eq_finrank_of_isSeparableproof · cited by 7
- taylorWithinEval_succproof · cited by 6
- Cardinal.mul_lt_aleph0proof · cited by 6
- padicValRat.mulproof · cited by 5
- DividedPowers.factorial_mul_dpow_eq_powproof · cited by 5
- Int.cast_negOnePow_natCastproof · cited by 5
Showing the 200 most cited of 310.