Theorems · Theorem · group theory
MulAction.IsBlock.smul_eq_smul_of_subset
∀ {G : Type u_1} {X : Type u_2} [inst : SMul G X] {B : Set X} {g₁ g₂ : G},
MulAction.IsBlock G B → g₁ • B ⊆ g₂ • B → g₁ • B = g₂ • B- Defined in
- Mathlib.GroupTheory.GroupAction.Blocks
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 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.
Cites5
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
- Set.smulSetstatement · cited by 608
- MulAction.IsBlockstatement and proof · cited by 73
- Set.smul_set_emptyproof · cited by 19
- Disjoint.eq_bot_of_leproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- MulAction.IsBlock.not_smul_set_ssubset_smul_setproof · cited by 0