Theorems · Theorem · order theory
OrderIso.isSimpleOrder_iff
∀ {α : Type u_2} {β : Type u_3} [inst : PartialOrder α] [inst_1 : PartialOrder β] [inst_2 : BoundedOrder α]
[inst_3 : BoundedOrder β] (f : α ≃o β), IsSimpleOrder α ↔ IsSimpleOrder β- Defined in
- Mathlib.Order.Atoms
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Top.topproof · cited by 9,680
- PartialOrderstatement and proof · cited by 6,410
- OrderIsostatement and proof · cited by 874
- BoundedOrderstatement and proof · cited by 270
- IsAtomproof · cited by 130
- IsSimpleOrderstatement and proof · cited by 54
- OrderIso.isAtom_iffproof · cited by 5
- OrderIso.map_topproof · cited by 4
- isSimpleOrder_iff_isAtom_topproof · cited by 3
Cited by12
Results whose statement or proof uses this declaration.
- isSimpleModule_iff_isAtomproof · cited by 7
- isSimpleModule_iff_isCoatomproof · cited by 6
- IsCompl.isAtom_iff_isCoatomproof · cited by 3
- OrderIso.isSimpleOrderproof · cited by 3
- RootPairing.isSimpleModule_weylGroupRootRep_iffproof · cited by 1
- simple_iff_isSimpleModuleproof · cited by 1
- Representation.isSimpleModule_iff_irreducible_ofModuleproof · cited by 1
- isSimpleModule_iff_isSimpleModule_of_algebraMap_surjectiveproof · cited by 1
- CategoryTheory.subobject_simple_iff_isAtomproof · cited by 1
- LinearMap.isSimpleModule_iff_of_bijectiveproof · cited by 0
- LieAlgebra.IsKilling.isSimple_iff_isIrreducibleproof · cited by 0
- Representation.irreducible_iff_isSimpleModule_asModuleproof · cited by 0