Theorems · Theorem · order theory
Nat.floor_lt_ceil_of_lt_of_pos
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [inst_2 : FloorSemiring R] [IsStrictOrderedRing R]
{a b : R}, a < b → 0 < b → ⌊a⌋₊ < ⌈b⌉₊- Defined in
- Mathlib.Algebra.Order.Floor.Semiring
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- LT.lt.leproof · cited by 2,189
- Nat.cast_zeroproof · cited by 1,870
- LT.lt.trans_leproof · cited by 678
- le_or_gtproof · cited by 269
- Nat.floorstatement · cited by 215
- FloorSemiringstatement and proof · cited by 179
- Nat.ceilstatement and proof · cited by 141
- Nat.le_ceilproof · cited by 38
- Nat.floor_ltproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.hausdorffMeasure_pi_realproof · cited by 3