Theorems · Theorem
Subtype.nontrivial_iff_exists_ne
∀ {α : Type u_1} (p : α → Prop) (x : Subtype p), Nontrivial (Subtype p) ↔ ∃ y, ∃ (_ : p y), y ≠ ↑x- Defined in
- Mathlib.Logic.Nontrivial.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nontrivialstatement · cited by 2,416
- nontrivial_iff_exists_neproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.nontrivial_iff_exists_ne_zeroproof · cited by 4
- Subgroup.nontrivial_iff_exists_ne_oneproof · cited by 4