Theorems · Theorem · order theory
Nat.lt_floor_add_one
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [inst_2 : FloorSemiring R] (a : R), a < ↑⌊a⌋₊ + 1- Defined in
- Mathlib.Algebra.Order.Floor.Semiring
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 27 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
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_addproof · cited by 586
- Nat.floorstatement and proof · cited by 215
- FloorSemiringstatement and proof · cited by 179
- Nat.lt_succ_floorproof · cited by 1
Cited by16
Results whose statement or proof uses this declaration.
- Nat.sub_one_lt_floorproof · cited by 5
- sum_mul_eq_sub_sub_integral_mulproof · cited by 4
- Nat.ceil_le_floor_add_oneproof · cited by 3
- MeasureTheory.hausdorffMeasure_pi_realproof · cited by 3
- Real.Gamma_ne_zeroproof · cited by 3
- integrableOn_mul_sum_Iccproof · cited by 3
- Real.summable_pow_div_factorialproof · cited by 1
- SzemerediRegularity.hundred_lt_pow_initialBound_mulproof · cited by 1
- Real.le_sum_ofDigitsTerm_digitsproof · cited by 1
- Nat.mul_lt_floorproof · cited by 1
- tendsto_nat_floor_mul_div_atTopproof · cited by 1
- Nat.abs_sub_floor_leproof · cited by 1