case h.e'_4
α : Type u_1
β : Type ?u.13935
L : List (List α)
i j : ℕ
hi : i < length L
hj : j < length (nthLe L i hi)
⊢ length (join L) = (fun i => sum (take i (map length L))) (length L)
α : Type u_1
β : Type ?u.13935
L : List (List α)
i j : ℕ
hi : i < length L
hj : j < length (nthLe L i hi)
⊢ sum (take i (map length L)) + j < length (join L)
convert lt_of_lt_of_le (sum_take_map_length_lt1 L hi hj) (monotone_sum_take _ hi)
case h.e'_4
α : Type u_1
β : Type ?u.13935
L : List (List α)
i j : ℕ
hi : i < length L
hj : j < length (nthLe L i hi)
this : length L = length (map length L)
⊢ length (join L) = (fun i => sum (take i (map length L))) (length L)
case h.e'_4
α : Type u_1
β : Type ?u.13935
L : List (List α)
i j : ℕ
hi : i < length L
hj : j < length (nthLe L i hi)
⊢ length (join L) = (fun i => sum (take i (map length L))) (length L)
have : L.length = (L.map length).length := by simp
no goals
case h.e'_4
α : Type u_1
β : Type ?u.13935
L : List (List α)
i j : ℕ
hi : i < length L
hj : j < length (nthLe L i hi)
this : length L = length (map length L)
⊢ length (join L) = (fun i => sum (take i (map length L))) (length L)
simp [this, -length_map]
no goals
α : Type u_1
β : Type ?u.13935
L : List (List α)
i j : ℕ
hi : i < length L
hj : j < length (nthLe L i hi)
⊢ length L = length (map length L)
simp