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Theorems · Theorem · group theory

SubMulAction.closure_le

∀ {R : Type u_1} {M : Type u_2} [inst : SMul R M] {s : Set M} {p : SubMulAction R M},
  SubMulAction.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
SMul
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Around this declaration

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

SemigroupIdeal.closure_le · cited by 1SemigroupIdeal.closure_leSubMulAction.closure_mono · cited by 1SubMulAction.closure_monoSet · cited by 53352SetSetLike.coe · cited by 8199SetLike.coeLE.le.trans · cited by 3151le.transSubMulAction · cited by 120SubMulActionSubMulAction.closure · cited by 6SubMulAction.closureSubMulAction.subset_closure · cited by 4SubMulAction.subset_closu…SubMulAction.mem_closure · cited by 3SubMulAction.mem_closureSubMulAction.closure_leCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.