Theorems · Definition · order theory

GroupConeClass.recOn

{S : Type u_1} →
  {G : Type u_2} →
    [inst : CommGroup G] →
      [inst_1 : SetLike S G] →
        {motive : GroupConeClass S G → Sort u} →
          (t : GroupConeClass S G) →
            ([toSubmonoidClass : SubmonoidClass S G] →
                (eq_one_of_mem_of_inv_mem : ∀ {C : S} {a : G}, a ∈ C → a⁻¹ ∈ C → a = 1) → motive ⋯) →
              motive t

Defined in: Mathlib.Algebra.Order.Group.Cone
Cited by: 0 results in Mathlib
Foundations: Depth 15 from the axioms · uses propext
Assumes: CommGroup SetLike

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SetLikestatement and proof · cited by 1,084
CommGroupstatement and proof · cited by 990
SubmonoidClassstatement and proof · cited by 60
GroupConeClassstatement and proof · cited by 3

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