Theorems · Theorem · commutative algebra
FiniteMultiplicity.multiplicity_add_of_gt
∀ {α : Type u_1} [inst : Ring α] {p a b : α},
FiniteMultiplicity p b → multiplicity p b < multiplicity p a → multiplicity p (a + b) = multiplicity p b- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- LT.lt.trans_leproof · cited by 678
- multiplicitystatement and proof · cited by 117
- FiniteMultiplicitystatement and proof · cited by 73
- FiniteMultiplicity.emultiplicity_eq_multiplicityproof · cited by 31
- WithTop.coe_strictMonoproof · cited by 8
- multiplicity_eq_of_emultiplicity_eqproof · cited by 8
- multiplicity_le_emultiplicityproof · cited by 5
- emultiplicity_add_of_gtproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- multiplicity_sub_of_gtproof · cited by 0
- multiplicity_add_eq_minproof · cited by 0