Theorems · Theorem · order theory
Nat.floor_le_floor
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [inst_2 : FloorSemiring R] {a b : R}
[IsStrictOrderedRing R], a ≤ b → ⌊a⌋₊ ≤ ⌊b⌋₊- Defined in
- Mathlib.Algebra.Order.Floor.Semiring
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
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
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Nat.floorstatement · cited by 215
- FloorSemiringstatement and proof · cited by 179
- Nat.floor_monoproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- sum_mul_eq_sub_sub_integral_mulproof · cited by 4
- integrableOn_mul_sum_Iccproof · cited by 3
- Chebyshev.sum_PrimePow_eq_sum_sum'proof · cited by 2