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Theorems · Theorem · commutative algebra

AdjoinRoot.induction_on

∀ {R : Type u_1} [inst : CommRing R] (f : Polynomial R) {C : AdjoinRoot f → Prop} (x : AdjoinRoot f),
  (∀ (p : Polynomial R), C ((AdjoinRoot.mk f) p)) → C x
Defined in
Mathlib.RingTheory.AdjoinRoot
Cited by
2 results in Mathlib
Foundations
Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRing
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AdjoinRoot.adjoinRoot_eq_top · cited by 4AdjoinRoot.adjoinRoot_eq_…AdjoinRoot.mk_leftInverse · cited by 0AdjoinRoot.mk_leftInverseDFunLike.coe · cited by 62936DFunLike.coeCommRing · cited by 17173CommRingRingHom · cited by 10189RingHomPolynomial · cited by 5681PolynomialAdjoinRoot · cited by 177AdjoinRootQuotient.inductionOn' · cited by 69Quotient.inductionOn'AdjoinRoot.mk · cited by 50AdjoinRoot.mkAdjoinRoot.induction_onCITED BYCITES

Cites7

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Cited by2

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