Let x0 of type ι be given.
Apply Eps_i_ex with
λ x1 . and (80242.. x1) (x0 = 236dc.. (ce322.. x0) x1).
Apply unknownprop_6430b6dff851fa455b9d955ead26232fc15e1a72a1ab4adf970f6e794cf870cd with
x0,
λ x1 . ∃ x2 . and (80242.. x2) (x1 = 236dc.. (ce322.. 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
80242.. x2,
236dc.. x1 x2 = 236dc.. (ce322.. (236dc.. x1 x2)) x2 leaving 2 subgoals.
The subproof is completed by applying H2.
Apply unknownprop_af5a8211ff947ff893b5035a5559a8e74e1503a79511eecb1f7a8d29e2eae278 with
x1,
x2,
λ x4 x5 . 236dc.. x1 x2 = 236dc.. 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.