Let x0 of type ι be given.
Apply Eps_i_ex with
λ x1 . and (SNo x1) (x0 = ad280.. (28f8d.. x0) x1).
Apply unknownprop_e73e07ecfeb5f0c05c137b34b758a03a6c1a818d92f2bc592020af36f35702e2 with
x0,
λ x1 . ∃ x2 . and (SNo x2) (x1 = ad280.. (28f8d.. x1) x2) leaving 2 subgoals.
The subproof is completed by applying H0.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ο be given.
Apply H4 with
x2.
Apply andI with
SNo x2,
ad280.. x1 x2 = ad280.. (28f8d.. (ad280.. x1 x2)) x2 leaving 2 subgoals.
The subproof is completed by applying H2.
Apply unknownprop_be33d753151483c7bac1e70b0036b153d449838792ed17caa64a7328dfc698e0 with
x1,
x2,
λ x4 x5 . ad280.. x1 x2 = ad280.. x5 x2 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Let x4 of type ι → ι → ο be given.
The subproof is completed by applying H5.