Theorems · Theorem · ring theory
RingCon.matrix_apply_single
∀ {R : Type u_1} (n : Type u_2) [inst : NonUnitalNonAssocSemiring R] [inst_1 : Fintype n] [inst_2 : DecidableEq n]
{c : RingCon R} {i j : n} {x y : R}, (RingCon.matrix n c) (Matrix.single i j x) (Matrix.single i j y) ↔ c x y- Defined in
- Mathlib.LinearAlgebra.Matrix.Ideal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Fintypestatement and proof · cited by 7,736
- Matrixstatement · cited by 4,303
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- RingConstatement and proof · cited by 219
- Matrix.singlestatement and proof · cited by 129
- ne_or_eqproof · cited by 32
- Matrix.single_apply_of_neproof · cited by 16
- Matrix.single_apply_sameproof · cited by 16
- RingCon.reflproof · cited by 10
- RingCon.matrixstatement and proof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- RingCon.ofMatrix_matrixproof · cited by 0