Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply unknownprop_389e2fb1855352fcc964ea44fe6723d7a1c2d512f04685300e3e97621725b977 with
nIn x2 x0,
nIn x2 x1 leaving 2 subgoals.
Apply unknownprop_b30a94f49240f0717f4ecb200a605aa8a4e6dad6dc5d1afa60c37866ee96baab with
x2,
x0.
Apply unknownprop_8369708f37c0d20e10b6156293f1b207e835dfc563ff7fbfa059bf26c84ddb80 with
x2,
binunion x0 x1 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_1598d20a62a395ced156dfcc7d767ab023594ea6ef7c5e3b53cecdbebaf0ec29 with
x0,
x1,
x2.
The subproof is completed by applying H1.
Apply unknownprop_b30a94f49240f0717f4ecb200a605aa8a4e6dad6dc5d1afa60c37866ee96baab with
x2,
x1.
Apply unknownprop_8369708f37c0d20e10b6156293f1b207e835dfc563ff7fbfa059bf26c84ddb80 with
x2,
binunion x0 x1 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_e6919c45bef19e01f88ce072c705412578331e9a3c7532de752ffb4187ed1265 with
x0,
x1,
x2.
The subproof is completed by applying H1.