Theorems · Theorem · order theory
Nat.ceil_eq_iff
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [inst_2 : FloorSemiring R] {a : R} {n : ℕ},
n ≠ 0 → (⌈a⌉₊ = n ↔ ↑(n - 1) < a ∧ a ≤ ↑n)- Defined in
- Mathlib.Algebra.Order.Floor.Semiring
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- not_leproof · cited by 328
- pos_iff_ne_zeroproof · cited by 180
- FloorSemiringstatement and proof · cited by 179
- Nat.ceilstatement and proof · cited by 141
- le_antisymm_iffproof · cited by 62
- Nat.ceil_leproof · cited by 15
- tsub_lt_iff_rightproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Int.clog_natCastproof · cited by 2
- Nat.preimage_ceil_of_ne_zeroproof · cited by 1
- NNRat.ceil_castproof · cited by 1