Theorems / mh_alge_c1cd6d

Mathlib held-out

Algebra · easy

Statement, exactly as the model and Lean see it
theorem lg_target {R : Type u_1} [Ring R] (M : ModuleCat R) [CategoryTheory.Simple M] : IsSimpleModule R ↑M := by
Mathlib declaration
isSimpleModule_of_simple
Held-out module
Mathlib.Algebra.Category.ModuleCat.Simple
Banned modules (itself + downstream)
2
Reference proof premises (reachable / held-out)
0 / 1

Traces

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No configuration has attempted this theorem yet.

Reference proof

Mathlib's own source for this declaration, shown for comparison. It may use lemmas the prover is not allowed to use.

/-- A simple object in the category of modules is a simple module. -/
instance isSimpleModule_of_simple (M : ModuleCat R) [Simple M] : IsSimpleModule R M :=
  simple_iff_isSimpleModule.mp ‹_›