Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply unknownprop_a818f53272de918398012791887b763f90bf043f961a4f625d98076ca0b8b392 with
In x2 (setsum x0 x1),
or (∃ x3 . and (In x3 x0) (x2 = setsum 0 x3)) (∃ x3 . and (In x3 x1) (x2 = setsum 1 x3)) leaving 2 subgoals.
The subproof is completed by applying unknownprop_c529973cb32f8d02a3950eda53e547d40c4a0e8faca1777353233a3377534f09 with x0, x1, x2.
Apply unknownprop_74210cc9b2960bdcb3eab56d0b4f5ba5a5771478f68cd794d919dafbcd157b00 with
λ x3 x4 : ι → ι . or (∃ x5 . and (In x5 x0) (x2 = x3 x5)) (∃ x5 . and (In x5 x1) (x2 = setsum 1 x5)) ⟶ In x2 (setsum x0 x1).
Apply unknownprop_e88b17fc7534a834a3292f38867e04234c9b0d119c42f884c32fbabae05b0d7e with
λ x3 x4 : ι → ι . or (∃ x5 . and (In x5 x0) (x2 = Inj0 x5)) (∃ x5 . and (In x5 x1) (x2 = x3 x5)) ⟶ In x2 (setsum x0 x1).
Apply unknownprop_eb8e8f72a91f1b934993d4cb19c84c8270f73a3626f3022b683d960a7fef89cb with
∃ x3 . and (In x3 x0) (x2 = Inj0 x3),
∃ x3 . and (In x3 x1) (x2 = Inj1 x3),
In x2 (setsum x0 x1) leaving 3 subgoals.
The subproof is completed by applying H0.
Assume H1:
∃ x3 . and (In x3 x0) (x2 = Inj0 x3).
Apply unknownprop_3848cfb1fd522cb609408da39f227a9c05924a24919f21041d0880590b824ef5 with
λ x3 . In x3 x0,
λ x3 . x2 = Inj0 x3,
In x2 (setsum x0 x1) leaving 2 subgoals.
The subproof is completed by applying H1.
Let x3 of type ι be given.
Apply H3 with
λ x4 x5 . In x5 (setsum x0 x1).
Apply unknownprop_1fbfebc9584f3b35fe974f93c7762fab1d5a4f649af5608ad307cbbc36ce4d37 with
x0,
x1,
x3.
The subproof is completed by applying H2.
Assume H1:
∃ x3 . and (In x3 x1) (x2 = Inj1 x3).
Apply unknownprop_3848cfb1fd522cb609408da39f227a9c05924a24919f21041d0880590b824ef5 with
λ x3 . In x3 x1,
λ x3 . x2 = Inj1 x3,
In x2 (setsum x0 x1) leaving 2 subgoals.
The subproof is completed by applying H1.
Let x3 of type ι be given.
Apply H3 with
λ x4 x5 . In x5 (setsum x0 x1).
Apply unknownprop_509aadde20bd8e655e679e36fea278577d08a1dbe475eed73f3fccc8c2d65f15 with
x0,
x1,
x3.
The subproof is completed by applying H2.