Theorems · Theorem · group theory
fixingAddSubmonoid_fixedPoints_gc
∀ (M : Type u_1) (α : Type u_2) [inst : AddMonoid M] [inst_1 : AddAction M α],
GaloisConnection (⇑OrderDual.toDual ∘ fixingAddSubmonoid M)
((fun P => AddAction.fixedPoints (↥P) α) ∘ ⇑OrderDual.ofDual)- Cited by
- 6 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Equivstatement · cited by 8,337
- Set.Elemproof · cited by 7,166
- AddMonoidstatement and proof · cited by 2,864
- AddSubmonoidstatement and proof · cited by 1,178
- OrderDualstatement and proof · cited by 927
- AddActionstatement and proof · cited by 820
- OrderDual.toDualstatement and proof · cited by 481
- OrderDual.ofDualstatement and proof · cited by 400
- GaloisConnectionstatement · cited by 253
- AddAction.fixedPointsstatement and proof · cited by 20
Cited by6
Results whose statement or proof uses this declaration.
- fixedPoints_addSubmonoid_iSupproof · cited by 0
- fixedPoints_addSubmonoid_supproof · cited by 0
- fixingAddSubmonoid_antitoneproof · cited by 0
- fixedPoints_antitone_addSubmonoidproof · cited by 0
- fixingAddSubmonoid_iUnionproof · cited by 0
- fixingAddSubmonoid_unionproof · cited by 0