Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply unknownprop_80056f9db85f84f8ce0644e1cdb62f5e66ec62c041f28dd7a07b3c46de1ea696 with
x2,
x0,
or (nIn x2 x0) (nIn x2 x1) leaving 2 subgoals.
Apply unknownprop_80056f9db85f84f8ce0644e1cdb62f5e66ec62c041f28dd7a07b3c46de1ea696 with
x2,
x1,
or (nIn x2 x0) (nIn x2 x1) leaving 2 subgoals.
Apply FalseE with
or (nIn x2 x0) (nIn x2 x1).
Apply unknownprop_8369708f37c0d20e10b6156293f1b207e835dfc563ff7fbfa059bf26c84ddb80 with
x2,
binintersect x0 x1 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_7e73699eda4c2a35af8db1aea1ddace7d2346405cd3944ace259823e1ec33cf3 with
x0,
x1,
x2 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply unknownprop_c29620ea10188dd8ed7659bc2875dc8e08f16ffd29713f8ee3146f02f9828ceb with
nIn x2 x0,
nIn x2 x1.
The subproof is completed by applying H2.
Apply unknownprop_7c688f24c3595bc4b513e911d7f551c8ccfedc804a6c15c02d25d01a2996aec6 with
nIn x2 x0,
nIn x2 x1.
The subproof is completed by applying H1.