Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply unknownprop_eb8e8f72a91f1b934993d4cb19c84c8270f73a3626f3022b683d960a7fef89cb with
∃ x3 . and (In x3 x0) (setsum 1 x2 = setsum 0 x3),
∃ x3 . and (In x3 x1) (setsum 1 x2 = setsum 1 x3),
In x2 x1 leaving 3 subgoals.
Apply unknownprop_c529973cb32f8d02a3950eda53e547d40c4a0e8faca1777353233a3377534f09 with
x0,
x1,
setsum 1 x2.
The subproof is completed by applying H0.
Apply unknownprop_74210cc9b2960bdcb3eab56d0b4f5ba5a5771478f68cd794d919dafbcd157b00 with
λ x3 x4 : ι → ι . (∃ x5 . and (In x5 x0) (setsum 1 x2 = x3 x5)) ⟶ In x2 x1.
Apply unknownprop_e88b17fc7534a834a3292f38867e04234c9b0d119c42f884c32fbabae05b0d7e with
λ x3 x4 : ι → ι . (∃ x5 . and (In x5 x0) (x3 x2 = Inj0 x5)) ⟶ In x2 x1.
Apply FalseE with
In x2 x1.
Apply unknownprop_3848cfb1fd522cb609408da39f227a9c05924a24919f21041d0880590b824ef5 with
λ x3 . In x3 x0,
λ x3 . Inj1 x2 = Inj0 x3,
False leaving 2 subgoals.
The subproof is completed by applying H1.
Let x3 of type ι be given.
Apply notE with
Inj0 x3 = Inj1 x2 leaving 2 subgoals.
The subproof is completed by applying unknownprop_2909aa42e9d0a354d060bc7d707070a586f9ab4666ef2c2e92d5cb1072a37e98 with x3, x2.
Let x4 of type ι → ι → ο be given.
The subproof is completed by applying H3 with λ x5 x6 . x4 x6 x5.
Apply unknownprop_e88b17fc7534a834a3292f38867e04234c9b0d119c42f884c32fbabae05b0d7e with
λ x3 x4 : ι → ι . (∃ x5 . and (In x5 x1) (x3 x2 = x3 x5)) ⟶ In x2 x1.
Apply unknownprop_3848cfb1fd522cb609408da39f227a9c05924a24919f21041d0880590b824ef5 with
λ x3 . In x3 x1,
λ x3 . Inj1 x2 = Inj1 x3,
In x2 x1 leaving 2 subgoals.
The subproof is completed by applying H1.
Let x3 of type ι be given.
Apply unknownprop_da82029798a5f9bbb993db5eff220fcf8fcae5b2fe3af56ebe878a8d8aeef3c3 with
x2,
x3,
λ x4 x5 . In x5 x1 leaving 2 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H2.