Theorems · Theorem · order theory
Nat.ceil_eq_zero
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [inst_2 : FloorSemiring R] {a : R}, ⌈a⌉₊ = 0 ↔ a ≤ 0- Defined in
- Mathlib.Algebra.Order.Floor.Semiring
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext
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
- Nat.cast_zeroproof · cited by 1,870
- FloorSemiringstatement and proof · cited by 179
- Nat.ceilstatement · cited by 141
- Nat.ceil_leproof · cited by 15
Cited by6
Results whose statement or proof uses this declaration.
- Nat.ceil_sub_natCastproof · cited by 3
- Int.log_of_right_le_zeroproof · cited by 3
- Real.BohrMollerup.tendsto_logGammaSeqproof · cited by 2
- SimpleGraph.triangleRemovalBound_nonposproof · cited by 1
- Nat.preimage_ceil_zeroproof · cited by 1
- Nat.ceil_lt_add_one_of_gt_neg_oneproof · cited by 0