Theorems · Theorem · order theory
Sublocale.restrict_of_mem
∀ {X : Type u_1} [inst : Order.Frame X] {S : Sublocale X} {a : X} (ha : a ∈ S), S.restrict a = ⟨a, ha⟩- Defined in
- Mathlib.Order.Sublocale
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Order.Frame
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.
- DFunLike.coestatement · cited by 62,936
- Order.Framestatement and proof · cited by 88
- FrameHomstatement · cited by 70
- GaloisInsertion.l_u_eqproof · cited by 37
- Sublocalestatement and proof · cited by 30
- Sublocale.restrictstatement · cited by 4
- Sublocale.giRestrictproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Sublocale.range_toNucleusproof · cited by 1