Let x0 of type ι be given.
Apply xm with
∃ x1 . prim1 x1 x0,
or (x0 = 4a7ef..) (∃ x1 . prim1 x1 x0) leaving 2 subgoals.
Assume H0:
∃ x1 . prim1 x1 x0.
Apply orIR with
x0 = 4a7ef..,
∃ x1 . prim1 x1 x0.
The subproof is completed by applying H0.
Apply orIL with
x0 = 4a7ef..,
∃ x1 . prim1 x1 x0.
Apply set_ext with
x0,
4a7ef.. leaving 2 subgoals.
Let x1 of type ι be given.
Apply FalseE with
prim1 x1 4a7ef...
Apply H0.
Let x2 of type ο be given.
Assume H2:
∀ x3 . prim1 x3 x0 ⟶ x2.
Apply H2 with
x1.
The subproof is completed by applying H1.
The subproof is completed by applying unknownprop_eb7b9ba678ea2ffa85e842fbfec0cd6c41d790582268f13f83a490db67168c54 with x0.