Theorems · Theorem · field theory
IntermediateField.AdjoinSimple.coe_aeval_gen_apply
∀ (F : Type u_1) [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] (α : E) (f : Polynomial F),
↑((Polynomial.aeval (IntermediateField.AdjoinSimple.gen F α)) f) = (Polynomial.aeval α) f- Cited by
- 3 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- AlgHomstatement · cited by 3,236
- IntermediateFieldstatement · cited by 988
- Polynomial.aevalstatement · cited by 615
- IntermediateField.adjoinstatement · cited by 382
- IntermediateField.AdjoinSimple.genstatement · cited by 55
- IntermediateField.mem_adjoin_simple_selfproof · cited by 19
- Polynomial.coe_aeval_mk_applyproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- RatFunc.algEquivOfTranscendental_algebraMapproof · cited by 3
- RatFunc.algEquivOfTranscendental_applyproof · cited by 1
- RatFunc.Luroth.algEquiv_algebraMapproof · cited by 0