Theorems · Theorem
List.tfae_of_cycle
∀ {a b : Prop} {l : List Prop},
List.IsChain (fun x1 x2 => x1 → x2) (a :: b :: l) → (l.getLastD b → a) → (a :: b :: l).TFAE- Defined in
- Mathlib.Data.List.TFAE
- Cited by
- 83 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- List.TFAEstatement and proof · cited by 102
Cited by83
Results whose statement or proof uses this declaration.
- IsLocalRing.local_hom_TFAEproof · cited by 10
- t1Space_TFAEproof · cited by 8
- CStarAlgebra.isStrictlyPositive_TFAEproof · cited by 7
- Ring.krullDimLE_zero_and_isLocalRing_tfaeproof · cited by 7
- CStarAlgebra.nonneg_TFAEproof · cited by 6
- LinearMap.normDet_ne_zero_tfaeproof · cited by 6
- specializes_TFAEproof · cited by 6
- regularSpace_TFAEproof · cited by 6
- IsLocallyConstant.tfaeproof · cited by 5
- RCLike.is_real_TFAEproof · cited by 5
- CategoryTheory.Functor.preservesFiniteLimits_tfaeproof · cited by 5
- CompleteLattice.wellFoundedGT_characterisationsproof · cited by 4