Let x0 of type ι be given.
Apply unknownprop_85336ee07ace71a942dc508d3b8c851d9d6bb88511443b7dafbf11b71c263f4d with
λ x1 . ∀ x2 x3 . aa8d2.. x1 x0 x2 ⟶ aa8d2.. x1 x0 x3 ⟶ x2 = x3 leaving 2 subgoals.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply unknownprop_6e6ce909b9c17abe947e3e080426f45a329a4c2db70cb2c91959a2db175cdfa8 with
x0,
x2,
λ x3 x4 . x1 = x4 leaving 2 subgoals.
The subproof is completed by applying H1.
Apply unknownprop_6e6ce909b9c17abe947e3e080426f45a329a4c2db70cb2c91959a2db175cdfa8 with
x0,
x1.
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 ι be given.
Apply unknownprop_bebd867283cf8e42ab0a6fcae40b7b03bd53172bba6a0231eb1c5875aaddede9 with
x1,
x0,
x2,
x2 = x3 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
Let x4 of type ι be given.
Apply H4 with
x2 = x3.
Assume H5:
x2 = prim3 x4.
Apply unknownprop_bebd867283cf8e42ab0a6fcae40b7b03bd53172bba6a0231eb1c5875aaddede9 with
x1,
x0,
x3,
x2 = x3 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H3.
Let x5 of type ι be given.
Apply H7 with
x2 = x3.
Assume H8:
x3 = prim3 x5.
Apply H5 with
λ x6 x7 . x7 = x3.
Apply H8 with
λ x6 x7 . prim3 x4 = x7.
Apply H1 with
x4,
x5,
λ x6 x7 . prim3 x7 = prim3 x5 leaving 3 subgoals.
The subproof is completed by applying H6.
The subproof is completed by applying H9.
Let x6 of type ι → ι → ο be given.
The subproof is completed by applying H10.