Theorems · Theorem · order theory
Nat.add_one_le_ceil_iff
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [inst_2 : FloorSemiring R] {a : R} {n : ℕ},
n + 1 ≤ ⌈a⌉₊ ↔ ↑n < a- Defined in
- Mathlib.Algebra.Order.Floor.Semiring
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- FloorSemiringstatement and proof · cited by 179
- Nat.ceilstatement and proof · cited by 141
- Nat.lt_ceilproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- ENat.le_ceilproof · cited by 1
- Nat.one_le_ceil_iffproof · cited by 0