simp only [map] at h
case cons.mk
κ : Type u_1
ν : Type u_2
k : κ
inst✝ : DecidableEq κ
kvs : List (κ × ν)
ih : k ∈ map Prod.fst (groupByKey kvs) → k ∈ map Prod.fst kvs
k₀ : κ
v₀ : ν
h : k ∈ map Prod.fst ((k₀, v₀ :: (matchKey kvs k₀).fst) :: groupByKey (matchKey kvs k₀).snd)
⊢ k ∈ map Prod.fst ((k₀, v₀) :: kvs)
case cons.mk
κ : Type u_1
ν : Type u_2
k : κ
inst✝ : DecidableEq κ
kvs : List (κ × ν)
ih : k ∈ map Prod.fst (groupByKey kvs) → k ∈ map Prod.fst kvs
k₀ : κ
v₀ : ν
h : k ∈ k₀ :: map Prod.fst (groupByKey (matchKey kvs k₀).snd)
⊢ k ∈ map Prod.fst ((k₀, v₀) :: kvs)