Theorems · Theorem
Equiv.nontrivial
∀ {α : Type u_1} {β : Type u_2} (e : α ≃ β) [Nontrivial β], Nontrivial α- Defined in
- Mathlib.Logic.Equiv.Defs
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses Quot.sound
- Assumes
- Nontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivstatement and proof · cited by 8,337
- Nontrivialstatement and proof · cited by 2,416
- Equiv.surjectiveproof · cited by 198
- Function.Surjective.nontrivialproof · cited by 4
Cited by8
Results whose statement or proof uses this declaration.
- Equiv.nontrivial_congrproof · cited by 3
- Module.FaithfullyFlat.iff_flat_and_lTensor_faithfulproof · cited by 2
- Module.FaithfullyFlat.iff_flat_and_rTensor_faithfulproof · cited by 2
- Module.support_quotientproof · cited by 1
- RootPairing.IsIrreducible.mk'proof · cited by 1
- Module.FaithfullyFlat.of_linearEquivproof · cited by 1
- CommRingCat.nontrivial_of_isPushout_of_isFieldproof · cited by 0