Theorems · Theorem · order theory
Nat.floor_one
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [inst_2 : FloorSemiring R] [IsStrictOrderedRing R],
⌊1⌋₊ = 1- Defined in
- Mathlib.Algebra.Order.Floor.Semiring
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
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
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Nat.floorstatement and proof · cited by 215
- FloorSemiringstatement and proof · cited by 179
- Nat.floor_natCastproof · cited by 19
Cited by6
Results whose statement or proof uses this declaration.
- Int.log_of_right_le_oneproof · cited by 8
- Complex.Gamma_zeroproof · cited by 7
- Int.clog_of_right_le_oneproof · cited by 2
- mul_pow_le_nat_floor_powproof · cited by 1
- sum_mul_eq_sub_integral_mul₀proof · cited by 1
- Int.log_one_rightproof · cited by 0