Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Let x2 of type ι be given.
Apply unknownprop_a818f53272de918398012791887b763f90bf043f961a4f625d98076ca0b8b392 with
In x2 (lam x0 (λ x3 . x1 x3)),
∃ x3 . and (In x3 x0) (∃ x4 . and (In x4 (x1 x3)) (x2 = setsum x3 x4)) leaving 2 subgoals.
The subproof is completed by applying unknownprop_f25818182af6b093121a8b5d43847162c8ea91396e524cca02557613a430a57a with x0, λ x3 . x1 x3, x2.
Assume H0:
∃ x3 . and (In x3 x0) (∃ x4 . and (In x4 (x1 x3)) (x2 = setsum x3 x4)).
Apply unknownprop_3848cfb1fd522cb609408da39f227a9c05924a24919f21041d0880590b824ef5 with
λ x3 . In x3 x0,
λ x3 . ∃ x4 . and (In x4 (x1 x3)) (x2 = setsum x3 x4),
In x2 (lam x0 (λ x3 . x1 x3)) leaving 2 subgoals.
The subproof is completed by applying H0.
Let x3 of type ι be given.
Assume H2:
∃ x4 . and (In x4 (x1 x3)) (x2 = setsum x3 x4).
Apply unknownprop_3848cfb1fd522cb609408da39f227a9c05924a24919f21041d0880590b824ef5 with
λ x4 . In x4 (x1 x3),
λ x4 . x2 = setsum x3 x4,
In x2 (lam x0 (λ x4 . x1 x4)) leaving 2 subgoals.
The subproof is completed by applying H2.
Let x4 of type ι be given.
Assume H3:
In x4 (x1 x3).
Apply H4 with
λ x5 x6 . In x6 (lam x0 (λ x7 . x1 x7)).
Apply unknownprop_1633a25a08ee627a1613041ad1ebe0a4535d0c6ce109cb609e7d9a519dad2f25 with
x0,
λ x5 . x1 x5,
x3,
x4 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H3.