Theorems · Theorem · group theory
AddSubsemigroup.mem_iSup_prop
∀ {M : Type u_2} [inst : Add M] {p : Prop} {S : p → AddSubsemigroup M} {x : M}, x ∈ ⨆ (h : p), S h ↔ ∃ (h : p), x ∈ S h- Cited by
- 0 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Add
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botproof · cited by 4,720
- iSupstatement · cited by 2,415
- AddSubsemigroupstatement and proof · cited by 262
- iSup_congr_Propproof · cited by 247
- iSup_posproof · cited by 61
- iSup_negproof · cited by 49
- IsEmpty.exists_iffproof · cited by 7
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.