Theorems · Theorem · order theory
Nat.floor_natCast
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [inst_2 : FloorSemiring R] [IsStrictOrderedRing R]
(n : ℕ), ⌊↑n⌋₊ = n- Defined in
- Mathlib.Algebra.Order.Floor.Semiring
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 38 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
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Nat.floorstatement · cited by 215
- FloorSemiringstatement and proof · cited by 179
- Nat.cast_leproof · cited by 159
- Nat.cast_nonnegproof · cited by 109
- eq_of_forall_le_iffproof · cited by 65
- Nat.le_floor_iffproof · cited by 24
Cited by19
Results whose statement or proof uses this declaration.
- Nat.floor_oneproof · cited by 6
- Nat.floor_zeroproof · cited by 6
- Int.log_natCastproof · cited by 3
- sum_mul_eq_sub_integral_mul'proof · cited by 2
- sum_mul_eq_sub_integral_mul₀'proof · cited by 2
- Chebyshev.psi_eq_psi_coe_floorproof · cited by 2
- Chebyshev.psi_eq_sum_mul_log_primeproof · cited by 2
- Complex.tendsto_one_add_pow_exp_of_tendstoproof · cited by 1
- Real.tendsto_one_add_pow_exp_of_tendstoproof · cited by 1
- Int.log_zpowproof · cited by 1
- Nat.floor_div_eq_divproof · cited by 1
- Nat.floor_ofNatproof · cited by 1