Theorems · Definition · group theory
MulAction.IsBlock
(G : Type u_1) → {X : Type u_2} → [SMul G X] → Set X → PropA set B is a G-block iff the sets of the form g • B are pairwise equal or disjoint.
- Defined in
- Mathlib.GroupTheory.GroupAction.Blocks
- Cited by
- 73 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SMul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by78
Results whose statement or proof uses this declaration.
- MulAction.IsPreprimitive.isTrivialBlock_of_isBlockstatement · cited by 9
- MulAction.IsPreprimitive.of_surjectiveproof · cited by 8
- MulAction.isPreprimitive_congrproof · cited by 6
- MulAction.IsBlock.preimagestatement and proof · cited by 5
- MulAction.IsBlock.translatestatement and proof · cited by 5
- MulAction.BlockMemproof · cited by 4
- MulAction.IsBlock.ncard_block_mul_ncard_orbit_eqstatement and proof · cited by 4
- MulAction.isBlock_iff_smul_eq_of_nonemptystatement · cited by 4
- MulAction.isBlock_iff_smul_eq_or_disjointstatement · cited by 4
- MulAction.IsBlock.eq_univ_of_card_ltstatement and proof · cited by 3
- MulAction.IsFixedBlock.isBlockstatement · cited by 3
- MulAction.isPreprimitive_of_is_two_pretransitiveproof · cited by 3