Theorems · Theorem · order theory
toIocDiv_natCast_mul_add
∀ {R : Type u_1} [inst : NonAssocRing R] [inst_1 : LinearOrder R] [inst_2 : IsOrderedAddMonoid R]
[inst_3 : Archimedean R] {p : R} (hp : 0 < p) (a b : R) (m : ℕ), toIocDiv hp a (↑m * p + b) = ↑m + toIocDiv hp a b- Defined in
- Mathlib.Algebra.Order.ToIntervalMod
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- Archimedeanstatement and proof · cited by 603
- NonAssocRingstatement and proof · cited by 483
- Int.cast_natCastproof · cited by 393
- toIocDivstatement and proof · cited by 85
- toIocDiv.congr_simpproof · cited by 21
- toIocDiv_intCast_mul_addproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- toIocDiv_ofNat_mul_addproof · cited by 0