Theorems · Theorem · field theory
RatFunc.isAlgebraic_adjoin_simple_X
∀ {K : Type u_1} [inst : Field K] (f : RatFunc K), (¬∃ c, f = RatFunc.C c) → IsAlgebraic (↥K⟮f⟯) RatFunc.X- Cited by
- 3 results in Mathlib
- Foundations
- Depth 135 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.
Cites13
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
- Setstatement · cited by 53,352
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- IntermediateFieldstatement · cited by 988
- IntermediateField.adjoinstatement and proof · cited by 382
- RatFuncstatement and proof · cited by 301
- IsAlgebraicstatement · cited by 163
- RatFunc.Xstatement · cited by 58
- RatFunc.Cstatement and proof · cited by 33
- RatFunc.minpolyXproof · cited by 12
- RatFunc.minpolyX_aeval_Xproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- RatFunc.finrank_eq_max_natDegreeproof · cited by 1
- RatFunc.IntermediateField.isAlgebraic_Xproof · cited by 0
- RatFunc.isAlgebraic_adjoin_simple_X'proof · cited by 0