Theorems · Theorem · group theory
MulAction.isInvariantBlock_iff_isFixedBlock
∀ {G : Type u_1} [inst : Group G] {X : Type u_2} [inst_1 : MulAction G X] {B : Set X},
MulAction.IsInvariantBlock G B ↔ MulAction.IsFixedBlock G BA block of a group action is invariant iff it is fixed.
- Defined in
- Mathlib.GroupTheory.GroupAction.Blocks
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 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.
- Setstatement and proof · cited by 53,352
- Groupstatement and proof · cited by 6,238
- MulActionstatement and proof · cited by 1,294
- LE.le.antisymmproof · cited by 507
- Set.subset_smul_set_iffproof · cited by 13
- MulAction.IsFixedBlockstatement · cited by 6
- MulAction.IsInvariantBlockstatement and proof · cited by 4
- MulAction.IsFixedBlock.isInvariantBlockproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- MulAction.IsInvariantBlock.isFixedBlockproof · cited by 1