Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Let x2 of type ι → ι → ι be given.
Let x3 of type ι be given.
Let x4 of type ι be given.
Assume H1:
In x4 (x1 x3).
Let x5 of type ι be given.
Assume H2:
In x5 (x2 x3 x4).
Apply unknownprop_bd19dfd009a9cdfd7e00e5a28a77c1545e733688b5ba89bd8cc2f4f90ec5aaa3 with
λ x6 x7 : ι → (ι → ι) → (ι → ι → ι) → ι . In (setsum x3 (setsum x4 x5)) (x7 x0 x1 x2).
Apply unknownprop_1633a25a08ee627a1613041ad1ebe0a4535d0c6ce109cb609e7d9a519dad2f25 with
x0,
λ x6 . lam (x1 x6) (x2 x6),
x3,
setsum x4 x5 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_1633a25a08ee627a1613041ad1ebe0a4535d0c6ce109cb609e7d9a519dad2f25 with
x1 x3,
x2 x3,
x4,
x5 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.