Theorems · Theorem · order theory
Nat.floor_le_ceil
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [inst_2 : FloorSemiring R] [IsStrictOrderedRing R]
(a : R), ⌊a⌋₊ ≤ ⌈a⌉₊- Defined in
- Mathlib.Algebra.Order.Floor.Semiring
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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.le.transproof · cited by 3,151
- IsStrictOrderedRingstatement and proof · cited by 2,490
- le_totalproof · cited by 294
- Nat.floorstatement · cited by 215
- FloorSemiringstatement and proof · cited by 179
- Nat.cast_leproof · cited by 159
- Nat.ceilstatement and proof · cited by 141
- Nat.le_ceilproof · cited by 38
- Nat.floor_leproof · cited by 21
- Nat.floor_of_nonposproof · cited by 9
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