Theorems · Theorem · group theory
MulAction.IsPreprimitive.isTrivialBlock_of_isBlock
∀ {G : Type u_1} {X : Type u_2} {inst : SMul G X} [self : MulAction.IsPreprimitive G X] {B : Set X},
MulAction.IsBlock G B → MulAction.IsTrivialBlock BAn action is preprimitive if it is pretransitive and the only blocks are the trivial ones
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MulAction.IsPreprimitive
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- MulAction.IsBlockstatement · cited by 73
- MulAction.IsPreprimitivestatement and proof · cited by 50
- MulAction.IsTrivialBlockstatement · cited by 15
Cited by9
Results whose statement or proof uses this declaration.
- MulAction.IsPreprimitive.of_surjectiveproof · cited by 8
- MulAction.isPreprimitive_congrproof · cited by 6
- MulAction.IsBlock.subsingleton_of_ssubset_of_stabilizer_leproof · cited by 2
- MulAction.IsBlock.subsingleton_of_stabilizer_lt_of_subsetproof · cited by 2
- MulAction.IsPreprimitive.exists_mem_smul_and_notMem_smulproof · cited by 1
- MulAction.IsPreprimitive.of_card_ltproof · cited by 1
- alternatingGroup.isTrivialBlock_of_isBlockproof · cited by 1
- MulAction.isSimpleOrder_blockMem_iff_isPreprimitiveproof · cited by 1
- MulAction.IsBlock.subsingleton_or_eq_univproof · cited by 0