Let x0 of type ι be given.
Let x1 of type ι be given.
Apply unknownprop_2c926b240fc658005337215abfdc8124a6f6eea17ba9f4df80d254bab3845972 with
λ x2 x3 : ι → ι → ο . x3 2 (lam 2 (λ x4 . If_i (x4 = 0) x0 x1)).
Let x2 of type ι be given.
Assume H0:
In x2 (lam 2 (λ x3 . If_i (x3 = 0) x0 x1)).
Apply unknownprop_f25818182af6b093121a8b5d43847162c8ea91396e524cca02557613a430a57a with
2,
λ x3 . If_i (x3 = 0) x0 x1,
x2.
The subproof is completed by applying H0.
Apply unknownprop_3848cfb1fd522cb609408da39f227a9c05924a24919f21041d0880590b824ef5 with
λ x3 . In x3 2,
λ x3 . ∃ x4 . and (In x4 (If_i (x3 = 0) x0 x1)) (x2 = setsum x3 x4),
∃ x3 . and (In x3 2) (∃ x4 . x2 = setsum x3 x4) leaving 2 subgoals.
The subproof is completed by applying L1.
Let x3 of type ι be given.
Apply unknownprop_3848cfb1fd522cb609408da39f227a9c05924a24919f21041d0880590b824ef5 with
λ x4 . In x4 (If_i (x3 = 0) x0 x1),
λ x4 . x2 = setsum x3 x4,
∃ x4 . and (In x4 2) (∃ x5 . x2 = setsum x4 x5) leaving 2 subgoals.
The subproof is completed by applying H3.
Let x4 of type ι be given.
Assume H4:
In x4 (If_i (x3 = 0) x0 x1).
Let x5 of type ο be given.
Assume H6:
∀ x6 . and (In x6 2) (∃ x7 . x2 = setsum x6 x7) ⟶ x5.
Apply H6 with
x3.
Apply unknownprop_389e2fb1855352fcc964ea44fe6723d7a1c2d512f04685300e3e97621725b977 with
In x3 2,
∃ x6 . x2 = setsum x3 x6 leaving 2 subgoals.
The subproof is completed by applying H2.
Let x6 of type ο be given.
Assume H7:
∀ x7 . x2 = setsum x3 x7 ⟶ x6.
Apply H7 with
x4.
The subproof is completed by applying H5.