Theorems · Theorem · order theory
Nat.lt_of_floor_lt
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [inst_2 : FloorSemiring R] {a : R} {n : ℕ},
⌊a⌋₊ < n → a < ↑n- Defined in
- Mathlib.Algebra.Order.Floor.Semiring
- Cited by
- 3 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.
Cites7
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
- lt_of_not_geproof · cited by 374
- Nat.floorstatement and proof · cited by 215
- LE.le.not_gtproof · cited by 189
- FloorSemiringstatement and proof · cited by 179
- Nat.le_floorproof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- Int.lt_zpow_succ_log_selfproof · cited by 1
- Nat.lt_succ_floorproof · cited by 1
- Nat.lt_one_of_floor_lt_oneproof · cited by 0