Let x0 of type ι be given.
Let x1 of type ι be given.
Apply unknownprop_48f8d4859b6b78ba3bbfab79f28064a8eb2fee8b3008bbf7332b70f58b78e189 with
λ x2 x3 : ι → ι . prim1 (x2 x1) x0.
Apply unknownprop_e546e9a8cc28c7314a8604ada98e2a83641f2ef6b8078441570ffe037b28d26f with
x0,
λ x2 . ∃ x3 . 09364.. x3 = x2,
158d3..,
x1,
prim1 (09364.. x1) x0 leaving 2 subgoals.
The subproof is completed by applying H0.
Let x2 of type ι be given.
Apply H2 with
prim1 (09364.. x1) x0.
Let x3 of type ι be given.
Apply H3 with
λ x4 x5 . prim1 (09364.. x5) x0.
Apply H4 with
λ x4 x5 . prim1 (09364.. (158d3.. x4)) x0.
Apply unknownprop_220466dabb9c90c9b087796465f1368ac3c1e9d1ef55643ebed4c27316fb8803 with
x3,
λ x4 x5 . prim1 (09364.. x5) x0.
Apply H4 with
λ x4 x5 . prim1 x5 x0.
The subproof is completed by applying H1.