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Theorems · Theorem · group theory

SubAddAction.closure_le

∀ {R : Type u_1} {M : Type u_2} [inst : VAdd R M] {s : Set M} {p : SubAddAction R M},
  SubAddAction.closure R s ≤ p ↔ s ⊆ ↑p
Defined in
Mathlib.GroupTheory.GroupAction.SubMulAction.Closure
Cited by
2 results in Mathlib
Foundations
Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
VAdd
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AddSemigroupIdeal.closure_le · cited by 1AddSemigroupIdeal.closure…SubAddAction.closure_mono · cited by 1SubAddAction.closure_monoSet · cited by 53352SetSetLike.coe · cited by 8199SetLike.coeLE.le.trans · cited by 3151le.transVAdd · cited by 616VAddSubAddAction · cited by 86SubAddActionSubAddAction.closure · cited by 6SubAddAction.closureSubAddAction.subset_closure · cited by 4SubAddAction.subset_closu…SubAddAction.mem_closure · cited by 3SubAddAction.mem_closureSubAddAction.closure_leCITED BYCITES

Cites8

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Cited by2

Results whose statement or proof uses this declaration.