Theorems · Theorem · field theory
RatFunc.Luroth.generator_ne_C
∀ {K : Type u_1} [inst : Field K] {E : IntermediateField K (RatFunc K)},
E ≠ ⊥ → ¬∃ c, RatFunc.Luroth.generator E = RatFunc.C c- Defined in
- Mathlib.FieldTheory.RatFunc.Luroth
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 143 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.
Cites9
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
- Bot.botstatement and proof · cited by 4,720
- IntermediateFieldstatement and proof · cited by 988
- RatFuncstatement and proof · cited by 301
- RatFunc.Cstatement and proof · cited by 33
- RatFunc.Luroth.generatorstatement and proof · cited by 11
- RatFunc.Luroth.generator_specproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- RatFunc.Luroth.transcendental_generatorproof · cited by 0
- RatFunc.Luroth.eq_adjoin_generatorproof · cited by 0
- RatFunc.Luroth.generator_ne_zeroproof · cited by 0