Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply iffI with
prim1 x2 (aae7a.. x0 x1),
or (∃ x3 . and (prim1 x3 x0) (x2 = aae7a.. 4a7ef.. x3)) (∃ x3 . and (prim1 x3 x1) (x2 = aae7a.. (4ae4a.. 4a7ef..) x3)) leaving 2 subgoals.
The subproof is completed by applying unknownprop_583e189228469f510dae093aa816b0d084f1acaf0341e7deab9d9a676d1b11ef with x0, x1, x2.
Apply unknownprop_669df0da86db4f986bae532f93288cb46feb5b77310c7f6de7766507585de4c6 with
λ x3 x4 : ι → ι . or (∃ x5 . and (prim1 x5 x0) (x2 = x3 x5)) (∃ x5 . and (prim1 x5 x1) (x2 = aae7a.. (4ae4a.. 4a7ef..) x5)) ⟶ prim1 x2 (aae7a.. x0 x1).
Apply unknownprop_48f8d4859b6b78ba3bbfab79f28064a8eb2fee8b3008bbf7332b70f58b78e189 with
λ x3 x4 : ι → ι . or (∃ x5 . and (prim1 x5 x0) (x2 = f6917.. x5)) (∃ x5 . and (prim1 x5 x1) (x2 = x3 x5)) ⟶ prim1 x2 (aae7a.. x0 x1).
Apply H0 with
prim1 x2 (aae7a.. x0 x1) leaving 2 subgoals.
Apply exandE_i with
λ x3 . prim1 x3 x0,
λ x3 . x2 = f6917.. x3,
prim1 x2 (aae7a.. x0 x1) leaving 2 subgoals.
The subproof is completed by applying H1.
Let x3 of type ι be given.
Apply H3 with
λ x4 x5 . prim1 x5 (aae7a.. x0 x1).
Apply unknownprop_8f6cc176a3f8bf2c7f1eddd738c1f22ef319b214b1baddc301c61e34c7bade15 with
x0,
x1,
x3.
The subproof is completed by applying H2.
Apply exandE_i with
λ x3 . prim1 x3 x1,
λ x3 . x2 = 09364.. x3,
prim1 x2 (aae7a.. x0 x1) leaving 2 subgoals.
The subproof is completed by applying H1.
Let x3 of type ι be given.
Apply H3 with
λ x4 x5 . prim1 x5 (aae7a.. x0 x1).
Apply unknownprop_21bfd05a2dded69408d4a77ad07f3965317c49d7fa73834904d6def11389f597 with
x0,
x1,
x3.
The subproof is completed by applying H2.