Theorems · Theorem · commutative algebra
emultiplicity_add_of_gt
∀ {α : Type u_1} [inst : Ring α] {p a b : α},
emultiplicity p b < emultiplicity p a → emultiplicity p (a + b) = emultiplicity p b- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- Ringstatement and proof · cited by 7,463
- ENatstatement and proof · cited by 4,985
- LT.lt.leproof · cited by 2,189
- emultiplicitystatement and proof · cited by 156
- multiplicityproof · cited by 117
- FiniteMultiplicityproof · cited by 73
- FiniteMultiplicity.emultiplicity_eq_multiplicityproof · cited by 31
- dvd_addproof · cited by 25
- Order.add_one_le_of_ltproof · cited by 13
- pow_dvd_of_le_emultiplicityproof · cited by 8
- FiniteMultiplicity.not_pow_dvd_of_multiplicity_ltproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- FiniteMultiplicity.multiplicity_add_of_gtproof · cited by 2
- emultiplicity_sub_of_gtproof · cited by 0
- emultiplicity_add_eq_minproof · cited by 0