Theorems · Theorem · field theory
IsAlgebraic.nontrivial
∀ {R : Type u} {A : Type v} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] {a : A},
IsAlgebraic R a → Nontrivial R- Defined in
- Mathlib.RingTheory.Algebraic.Basic
- Cited by
- 5 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Nontrivialstatement · cited by 2,416
- IsAlgebraicstatement and proof · cited by 163
- is_transcendental_of_subsingletonproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- Algebra.IsAlgebraic.nontrivialproof · cited by 5
- IsTranscendenceBasis.of_isAlgebraic_adjoin_insert_sdiffproof · cited by 2
- IsAlgebraic.adjoin_of_forall_isAlgebraicproof · cited by 1
- Algebra.isAlgebraic_adjoin_of_nonemptyproof · cited by 1
- IsAlgebraic.powproof · cited by 0