Theorems · Theorem · order theory
Nat.le_ceil
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [inst_2 : FloorSemiring R] (a : R), a ≤ ↑⌈a⌉₊- Defined in
- Mathlib.Algebra.Order.Floor.Semiring
- Cited by
- 38 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- le_rflproof · cited by 1,558
- FloorSemiringstatement and proof · cited by 179
- Nat.ceilstatement · cited by 141
- Nat.ceil_leproof · cited by 15
Cited by38
Results whose statement or proof uses this declaration.
- NumberField.Embeddings.finite_of_norm_leproof · cited by 4
- SchwartzMap.isBigO_cocompact_rpowproof · cited by 3
- Real.tendsto_exp_div_pow_atTopproof · cited by 3
- Real.exists_isLUBproof · cited by 3
- Real.BohrMollerup.tendsto_logGammaSeqproof · cited by 2
- archimedean_iff_rat_ltproof · cited by 2
- tendsto_nat_ceil_mul_div_atTopproof · cited by 2
- Liouville.liouvilleWithproof · cited by 2
- Complex.eventually_atTop_regularizedHGFunCoeff_ne_zeroproof · cited by 2
- SimpleGraph.FarFromTriangleFree.le_card_cliqueFinsetproof · cited by 2
- Rat.AbsoluteValue.eq_one_of_not_dvdproof · cited by 1
- AkraBazziRecurrence.rpow_p_mul_one_add_smoothingFn_geproof · cited by 1