Theorems · Definition · ring theory

SemilinearMapClass.recOn

{F : Type u_14} →
  {R : Type u_15} →
    {S : Type u_16} →
      [inst : Semiring R] →
        [inst_1 : Semiring S] →
          {σ : R →+* S} →
            {M : Type u_17} →
              {M₂ : Type u_18} →
                [inst_2 : AddCommMonoid M] →
                  [inst_3 : AddCommMonoid M₂] →
                    [inst_4 : Module R M] →
                      [inst_5 : Module S M₂] →
                        [inst_6 : FunLike F M M₂] →
                          {motive : SemilinearMapClass F σ M M₂ → Sort u} →
                            (t : SemilinearMapClass F σ M M₂) →
                              ([toAddHomClass : AddHomClass F M M₂] →
                                  [toMulActionSemiHomClass : MulActionSemiHomClass F (⇑σ) M M₂] → motive ⋯) →
                                motive t

Defined in

Mathlib.Algebra.Module.LinearMap.Defs

Cited by

0 results in Mathlib

Foundations

Depth 18 from the axioms · uses no axioms

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidModuleModuleFunLike