Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply unknownprop_583e189228469f510dae093aa816b0d084f1acaf0341e7deab9d9a676d1b11ef with
x0,
x1,
aae7a.. (4ae4a.. 4a7ef..) x2,
prim1 x2 x1 leaving 3 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_669df0da86db4f986bae532f93288cb46feb5b77310c7f6de7766507585de4c6 with
λ x3 x4 : ι → ι . (∃ x5 . and (prim1 x5 x0) (aae7a.. (4ae4a.. 4a7ef..) x2 = x3 x5)) ⟶ prim1 x2 x1.
Apply unknownprop_48f8d4859b6b78ba3bbfab79f28064a8eb2fee8b3008bbf7332b70f58b78e189 with
λ x3 x4 : ι → ι . (∃ x5 . and (prim1 x5 x0) (x3 x2 = f6917.. x5)) ⟶ prim1 x2 x1.
Apply FalseE with
prim1 x2 x1.
Apply exandE_i with
λ x3 . prim1 x3 x0,
λ x3 . 09364.. x2 = f6917.. x3,
False leaving 2 subgoals.
The subproof is completed by applying H1.
Let x3 of type ι be given.
Apply unknownprop_eb2fcd306f6f841b66fd8e32d0e8a446cfe3594d26b0bbf0192de86d9ef1a8f4 with
x3,
x2.
Let x4 of type ι → ι → ο be given.
The subproof is completed by applying H3 with λ x5 x6 . x4 x6 x5.
Apply unknownprop_48f8d4859b6b78ba3bbfab79f28064a8eb2fee8b3008bbf7332b70f58b78e189 with
λ x3 x4 : ι → ι . (∃ x5 . and (prim1 x5 x1) (x3 x2 = x3 x5)) ⟶ prim1 x2 x1.
Apply exandE_i with
λ x3 . prim1 x3 x1,
λ x3 . 09364.. x2 = 09364.. x3,
prim1 x2 x1 leaving 2 subgoals.
The subproof is completed by applying H1.
Let x3 of type ι be given.
Apply unknownprop_47e41120ef0e6cbc7dee61e4e0adec283cb1cf9d56967690cc69f7192955cae0 with
x2,
x3,
λ x4 x5 . prim1 x5 x1 leaving 2 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H2.