Theorems · Theorem · order theory
ENat.natCast_add
∀ (m n : ℕ), ↑(m + n) = ↑m + ↑n
- Defined in
- Mathlib.Data.ENat.Basic
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENatstatement · cited by 4,985
Cited by17
Results whose statement or proof uses this declaration.
- Fin.Embedding.restrictSurjective_of_add_le_natCardproof · cited by 3
- Order.height_le_of_krullDim_preimage_leproof · cited by 2
- Polynomial.natTrailingDegree_mul'proof · cited by 2
- Fin.Embedding.exists_embedding_disjoint_range_of_add_le_ENat_cardproof · cited by 2
- PowerSeries.order_mulproof · cited by 2
- SimpleGraph.Reachable.dist_triangle_leftproof · cited by 1
- SimpleGraph.Reachable.dist_triangle_rightproof · cited by 1
- ENat.WithBot.add_one_le_iffproof · cited by 1
- Polynomial.trailingDegree_mul'proof · cited by 1
- analyticOrderAt_smulproof · cited by 1
- Dynamics.coverMincard_union_leproof · cited by 1