Theorems · Definition · commutative algebra

Module.FinitePresentation.casesOn

{R : Type u_1} →
  {M : Type u_2} →
    [inst : Semiring R] →
      [inst_1 : AddCommMonoid M] →
        [inst_2 : Module R M] →
          {motive : Module.FinitePresentation R M → Sort u} →
            (t : Module.FinitePresentation R M) →
              ((out : ∃ s, Submodule.span R ↑s = ⊤ ∧ (Finsupp.linearCombination R Subtype.val).ker.FG) → motive ⋯) →
                motive t

Defined in

Mathlib.Algebra.Module.FinitePresentation

Cited by

3 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModule