Theorems · Theorem · order theory
ENat.natCast_toNat
∀ {n : ℕ∞}, n ≠ ⊤ → ↑n.toNat = nAlias of the reverse direction of ENat.natCast_toNat_eq_self.
- Defined in
- Mathlib.Data.ENat.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
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.
- Top.topstatement · cited by 9,680
- ENatstatement and proof · cited by 4,985
- ENat.toNatstatement · cited by 143
- ENat.natCast_toNat_eq_selfproof · cited by 9
Cited by11
Results whose statement or proof uses this declaration.
- Polynomial.trailingDegree_eq_natTrailingDegreeproof · cited by 8
- ENat.toNat_le_toNatproof · cited by 6
- Nat.cast_analyticOrderNatAtproof · cited by 2
- MvPowerSeries.weightedOrder_mulproof · cited by 2
- Set.Finite.encard_eq_coeproof · cited by 1
- Ideal.exists_spanRank_eq_and_height_eqproof · cited by 1
- Nat.count_le_setNCardproof · cited by 0
- SimpleGraph.Reachable.coe_dist_eq_edistproof · cited by 0
- ENat.coe_toNatproof · cited by 0
- Ring.ordMonoidHom_eq_ordproof · cited by 0
- ENat.toNat_sumproof · cited by 0