Let x0 of type ι be given.
Let x1 of type ι be given.
Apply unknownprop_c5e2164052a280ad5b04f622e53815f0267ee33361e4345305e43303abef2c1b with
2,
λ x2 . If_i (x2 = 0) x0 x1,
0,
λ x2 x3 . x3 = x0 leaving 2 subgoals.
The subproof is completed by applying unknownprop_7630054952f4bd54be6e25e2e786a4db7b90ee782d6b1031afa63aeb6d55b595.
Apply unknownprop_6f44febdf8a865ee94133af873e3c2941a931de6ac80968301360290e02ca608 with
0 = 0,
x0,
x1.
Let x2 of type ι → ι → ο be given.
Assume H0: x2 0 0.
The subproof is completed by applying H0.