Theorems · Theorem · order theory
Nat.lt_ceil
∀ {α : Type u_2} [inst : Semiring α] [inst_1 : LinearOrder α] [inst_2 : FloorSemiring α] {a : α} {n : ℕ},
n < ⌈a⌉₊ ↔ ↑n < a- Defined in
- Mathlib.Algebra.Order.Floor.Defs
- Cited by
- 10 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
- FloorSemiringstatement and proof · cited by 179
- Nat.ceilstatement · cited by 141
- lt_iff_lt_of_le_iff_leproof · cited by 54
- Nat.ceil_leproof · cited by 15
Cited by10
Results whose statement or proof uses this declaration.
- Nat.ceil_lt_add_oneproof · cited by 11
- Nat.ceil_add_natCastproof · cited by 4
- Nat.ceil_posproof · cited by 4
- Real.tendsto_exp_div_pow_atTopproof · cited by 3
- Nat.add_one_le_ceil_iffproof · cited by 2
- Nat.floor_lt_ceil_of_lt_of_posproof · cited by 1
- Behrend.three_le_nValueproof · cited by 1
- Int.lt_zpow_succ_log_selfproof · cited by 1
- Behrend.boundproof · cited by 1
- Nat.closedBall_eq_Iccproof · cited by 0