Let x0 of type ι be given.
Apply unknownprop_1fe1f9b87156c35e13519655d4a61e2c6dea7ba3e9716ca13f2c1f009fc9c17d with
x0,
λ x1 x2 . or (and (x1 = 4a7ef..) (x2 = x0)) (∃ x3 x4 . and (and (x1 = 4ae4a.. x3) (x2 = prim3 x4)) (aa8d2.. x3 x0 x4)) leaving 2 subgoals.
Apply orIL with
and (4a7ef.. = 4a7ef..) (x0 = x0),
∃ x1 x2 . and (and (4a7ef.. = 4ae4a.. x1) (x0 = prim3 x2)) (aa8d2.. x1 x0 x2).
Apply andI with
4a7ef.. = 4a7ef..,
x0 = x0 leaving 2 subgoals.
Let x1 of type ι → ι → ο be given.
The subproof is completed by applying H0.
Let x1 of type ι → ι → ο be given.
Assume H0: x1 x0 x0.
The subproof is completed by applying H0.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply orIR with
and (4ae4a.. x1 = 4a7ef..) (prim3 x2 = x0),
∃ x3 x4 . and (and (4ae4a.. x1 = 4ae4a.. x3) (prim3 x2 = prim3 x4)) (aa8d2.. x3 x0 x4).
Let x3 of type ο be given.
Apply H3 with
x1.
Let x4 of type ο be given.
Apply H4 with
x2.
Apply and3I with
4ae4a.. x1 = 4ae4a.. x1,
prim3 x2 = prim3 x2,
aa8d2.. x1 x0 x2 leaving 3 subgoals.
Let x5 of type ι → ι → ο be given.
The subproof is completed by applying H5.
Let x5 of type ι → ι → ο be given.
The subproof is completed by applying H5.
The subproof is completed by applying H1.