Theorems · Theorem · order theory
Nucleus.mem_range
∀ {X : Type u_1} [inst : Order.Frame X] {n : Nucleus X} {x : X}, x ∈ Set.range ⇑n ↔ n x = x- Defined in
- Mathlib.Order.Nucleus
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 22 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Set.rangestatement and proof · cited by 4,705
- Order.Framestatement and proof · cited by 88
- Nucleusstatement and proof · cited by 41
- Nucleus.idempotentproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Nucleus.range_subset_rangeproof · cited by 0