Theorems · Theorem · order theory
Int.floor_zero
∀ {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : FloorRing R] [IsOrderedRing R], ⌊0⌋ = 0- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 51 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.
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- IsOrderedRingstatement and proof · cited by 777
- FloorRingstatement and proof · cited by 405
- Int.floorstatement and proof · cited by 225
- Int.cast_zeroproof · cited by 188
- Int.floor_intCastproof · cited by 14
Cited by6
Results whose statement or proof uses this declaration.
- Int.fract_zeroproof · cited by 6
- Real.exists_int_int_abs_mul_sub_leproof · cited by 2
- round_zeroproof · cited by 2
- Real.floor_logb_natCastproof · cited by 2
- Real.convergent_of_zeroproof · cited by 1
- Int.floor_div_cast_of_nonnegproof · cited by 1