Theorems · Theorem · commutative algebra
multiplicity_add_eq_min
∀ {α : Type u_1} [inst : Ring α] {p a b : α},
FiniteMultiplicity p a →
FiniteMultiplicity p b →
multiplicity p a ≠ multiplicity p b → multiplicity p (a + b) = min (multiplicity p a) (multiplicity p b)- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
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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
- add_commproof · cited by 1,535
- le_of_ltproof · cited by 1,175
- lt_trichotomyproof · cited by 178
- multiplicitystatement and proof · cited by 117
- FiniteMultiplicitystatement and proof · cited by 73
- min_eq_leftproof · cited by 67
- min_eq_rightproof · cited by 54
- FiniteMultiplicity.multiplicity_add_of_gtproof · cited by 2
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