Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Assume H1:
In x3 (x1 x2).
Apply unknownprop_17fe3de18bc1fbdc28d994143167b7a573f559855ba378d2014a681d31fa93ad with
λ x4 x5 : ι → (ι → ι) → ι . In (setsum x2 x3) (x5 x0 (λ x6 . x1 x6)).
Apply unknownprop_4d9a081a15fdc79c67eee9fe67650a775bc97737c16f9cc2a1a6fdd7a2cc8108 with
x0,
λ x4 . Repl (x1 x4) (λ x5 . setsum x4 x5),
x2,
setsum x2 x3 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_63c308b92260dbfca8c9530846e6836ba3e6be221cc8e80fd61db913e01bdacf with
x1 x2,
setsum x2,
x3.
The subproof is completed by applying H1.