Theorems · Theorem · order theory
Nat.floor_le
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [inst_2 : FloorSemiring R] {a : R}, 0 ≤ a → ↑⌊a⌋₊ ≤ a- Defined in
- Mathlib.Algebra.Order.Floor.Semiring
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 21 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
- Nat.floorstatement · cited by 215
- FloorSemiringstatement and proof · cited by 179
- Nat.le_floor_iffproof · cited by 24
Cited by21
Results whose statement or proof uses this declaration.
- Nat.floor_monoproof · cited by 8
- sum_mul_eq_sub_sub_integral_mulproof · cited by 4
- Chebyshev.theta_le_log4_mul_xproof · cited by 4
- MeasureTheory.hausdorffMeasure_pi_realproof · cited by 3
- integrableOn_mul_sum_Iccproof · cited by 3
- Nat.floor_sub_natCastproof · cited by 3
- Chebyshev.psi_ge'proof · cited by 2
- Chebyshev.psi_le_primeCounting_mul_log'proof · cited by 2
- Chebyshev.abs_psi_sub_theta_le_sqrt_mul_logproof · cited by 2
- Behrend.le_Nproof · cited by 1
- Int.Matrix.exists_ne_zero_int_vec_norm_leproof · cited by 1
- Nat.floor_congrproof · cited by 1