Theorems · Theorem
nontrivial_iff_exists_ne
∀ {α : Type u_1} (x : α), Nontrivial α ↔ ∃ y, y ≠ x- Defined in
- Mathlib.Logic.Nontrivial.Defs
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nontrivialstatement and proof · cited by 2,416
- exists_neproof · cited by 101
- nontrivial_of_neproof · cited by 14
Cited by8
Results whose statement or proof uses this declaration.
- rank_pos_iff_nontrivialproof · cited by 4
- Subtype.nontrivial_iff_exists_neproof · cited by 2
- AddSubmonoid.nontrivial_iff_exists_ne_zeroproof · cited by 2
- CategoryTheory.finrank_hom_simple_simple_le_oneproof · cited by 2
- NNReal.exists_lt_of_strictMonoproof · cited by 2
- Submonoid.nontrivial_iff_exists_ne_oneproof · cited by 1
- notMem_iff_exists_ne_and_isConjRootproof · cited by 1
- Cardinal.two_le_iff'proof · cited by 0