Theorems · Theorem · functional analysis
continuous_negPart
∀ {α : Type u_1} [inst : NormedAddCommGroup α] [inst_1 : Lattice α] [HasSolidNorm α] [IsOrderedAddMonoid α],
Continuous negPart- Defined in
- Mathlib.Analysis.Normed.Order.Lattice
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 158 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.
- NormedAddCommGroupstatement and proof · cited by 15,752
- Continuousstatement · cited by 2,592
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- Latticestatement and proof · cited by 916
- NegPart.negPartstatement · cited by 107
- HasSolidNormstatement and proof · cited by 67
- LipschitzWith.continuousproof · cited by 30
- lipschitzWith_negPartproof · cited by 1
Cited by9
Results whose statement or proof uses this declaration.
- CFC.posPart_sub_negPartproof · cited by 10
- CFC.posPart_add_negPartproof · cited by 2
- spectrum_star_mul_self_nonnegproof · cited by 1
- CFC.negPart_mul_posPartproof · cited by 1
- isClosed_nonnegproof · cited by 0
- IsSelfAdjoint.norm_eq_max_norm_posPart_negPartproof · cited by 0
- CFC.posPart_mul_negPartproof · cited by 0
- CFC.negPart_algebraMapproof · cited by 0
- CFC.negPart_oneproof · cited by 0