Theorems · Theorem · order theory
Nat.ceil_natCast
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [inst_2 : FloorSemiring R] [IsStrictOrderedRing R]
(n : ℕ), ⌈↑n⌉₊ = n- Defined in
- Mathlib.Algebra.Order.Floor.Semiring
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- LinearOrderstatement and proof · cited by 8,572
- IsStrictOrderedRingstatement and proof · cited by 2,490
- FloorSemiringstatement and proof · cited by 179
- Nat.cast_leproof · cited by 159
- Nat.ceilstatement · cited by 141
- eq_of_forall_ge_iffproof · cited by 96
- Nat.ceil_leproof · cited by 15
Cited by6
Results whose statement or proof uses this declaration.
- Nat.ceil_oneproof · cited by 6
- Nat.ceil_zeroproof · cited by 3
- tendsto_nat_ceil_atTopproof · cited by 1
- Int.log_zpowproof · cited by 1
- Mathlib.Meta.NormNum.IsNat.natCeilproof · cited by 0
- Nat.ceil_ofNatproof · cited by 0