Theorems · Theorem · field theory
RatFunc.transcendental_of_ne_C
∀ {K : Type u_1} [inst : Field K] (f : RatFunc K), (¬∃ c, f = RatFunc.C c) → Transcendental K f- Cited by
- 3 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- IntermediateField.adjoinproof · cited by 382
- Algebra.IsAlgebraicproof · cited by 322
- RatFuncstatement and proof · cited by 301
- IsAlgebraicproof · cited by 163
- Transcendentalstatement · cited by 91
- RatFunc.Cstatement and proof · cited by 33
- IsAlgebraic.isIntegralproof · cited by 25
- Algebra.Transcendentalproof · cited by 17
- Algebra.IsAlgebraic.transproof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- RatFunc.irreducible_minpolyXproof · cited by 1
- RatFunc.irreducible_minpolyX'proof · cited by 1
- RatFunc.Luroth.transcendental_generatorproof · cited by 0