Theorems · Theorem · combinatorics
not_finite
∀ (α : Sort u_3) [Infinite α] [Finite α], False
Infinite α is not Finite
- Defined in
- Mathlib.Data.Finite.Defs
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
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.
- Finitestatement and proof · cited by 3,029
- Infinitestatement and proof · cited by 352
- Infinite.not_finiteproof · cited by 5
Cited by10
Results whose statement or proof uses this declaration.
- ZMod.cardproof · cited by 36
- Fintype.falseproof · cited by 5
- Finite.falseproof · cited by 3
- RootPairing.coxeterWeight_ne_four_of_linearIndependentproof · cited by 1
- Subspace.biUnion_ne_univ_of_top_notMemproof · cited by 1
- ConnectedComponents.exists_fun_isClopen_of_infiniteproof · cited by 1
- summable_const_iffproof · cited by 1
- AlgHom.IsArithFrobAt.finite_quotientproof · cited by 1
- multipliable_const_iffproof · cited by 0
- Module.Finite.not_linearIndependent_of_infiniteproof · cited by 0