Theorems · Definition · group theory

AddAction.QuotientAction.casesOn

{G : Type u} →
  {X : Type v} →
    [inst : AddGroup G] →
      [inst_1 : AddMonoid X] →
        [inst_2 : AddAction X G] →
          {H : AddSubgroup G} →
            {motive : AddAction.QuotientAction X H → Sort u_1} →
              (t : AddAction.QuotientAction X H) →
                ((inv_mul_mem : ∀ (x : X) {g g' : G}, -g + g' ∈ H → -(x +ᵥ g) + (x +ᵥ g') ∈ H) → motive ⋯) → motive t

Defined in

Mathlib.GroupTheory.GroupAction.Quotient

Cited by

0 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext

Assumes

AddGroupAddMonoidAddAction