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Theorems · Definition · commutative algebra

Function.Surjective.distrib

{R : Type u_1} →
  {S : Type u_2} →
    (f : R → S) →
      Function.Surjective f →
        [inst : Add S] →
          [inst_1 : Mul S] →
            [inst_2 : Distrib R] →
              (∀ (x y : R), f (x + y) = f x + f y) → (∀ (x y : R), f (x * y) = f x * f y) → Distrib S

Pushforward a Distrib instance along a surjective function.

Defined in
Mathlib.Algebra.Ring.InjSurj
Cited by
0 results in Mathlib
Foundations
Depth 10 from the axioms · uses propext
Assumes
AddMulDistrib
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Around this declaration

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

Function.Surjective.nonUnitalNonAssocSemiring · cited by 0Surjective.nonUnitalNonAs…Distrib · cited by 31DistribLeftDistribClass · cited by 12LeftDistribClassRightDistribClass · cited by 11RightDistribClassRightDistribClass.right_distrib · cited by 2RightDistribClass.right_d…LeftDistribClass.left_distrib · cited by 1LeftDistribClass.left_dis…Surjective.distribCITED BYCITES

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