Theorems · Theorem · field theory
Polynomial.X_mul_C
∀ {R : Type u} [inst : Semiring R] (r : R), Polynomial.X * Polynomial.C r = Polynomial.C r * Polynomial.XPrefer putting constants to the left of X.
This lemma is the loop-avoiding simp version of Polynomial.X_mul.
- Defined in
- Mathlib.Algebra.Polynomial.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- Polynomialstatement · cited by 5,681
- Polynomial.Xstatement · cited by 1,639
- Polynomial.Cstatement · cited by 1,598
- Polynomial.X_mulproof · cited by 12
Cited by9
Results whose statement or proof uses this declaration.
- RatFunc.irreducible_minpolyX'proof · cited by 1
- Polynomial.isLeftCancelMulZero_iffproof · cited by 1
- Matrix.eval_charpolyRevproof · cited by 1
- Matrix.det_one_add_smulproof · cited by 1
- Polynomial.coeff_det_X_add_C_cardproof · cited by 1
- Matrix.derivative_det_one_add_X_smul_auxproof · cited by 1
- StandardEtalePresentation.toPresentation_relationproof · cited by 1
- Matrix.derivative_det_one_add_X_smulproof · cited by 0
- Polynomial.coeff_det_X_add_C_zeroproof · cited by 0