Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = dd3c8.. (f482f.. x1 4a7ef..) (2b2e3.. (f482f.. x1 (4ae4a.. 4a7ef..))) (f482f.. x1 (4ae4a.. (4ae4a.. 4a7ef..))).
Let x1 of type ι be given.
Let x2 of type ι → ι → ο be given.
Let x3 of type ι be given.
Apply unknownprop_80b971e1e769c036da944ad596d7d907ce651d9af374e9c7a1d04d6f88668c42 with
x1,
x2,
x3,
λ x4 x5 . dd3c8.. x1 x2 x3 = dd3c8.. x4 (2b2e3.. (f482f.. (dd3c8.. x1 x2 x3) (4ae4a.. 4a7ef..))) (f482f.. (dd3c8.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))).
Apply unknownprop_f1e6338dba9d8a4b13d4526138bc59bec058c063c6bea746ef372dfd89320783 with
x1,
x2,
x3,
λ x4 x5 . dd3c8.. x1 x2 x3 = dd3c8.. x1 (2b2e3.. (f482f.. (dd3c8.. x1 x2 x3) (4ae4a.. 4a7ef..))) x4.
Apply unknownprop_0e45ffe32b70ce36d82c9a63ab95f4a34e025cfc2821239a4bfc708f9fe886ab with
x1,
x2,
2b2e3.. (f482f.. (dd3c8.. x1 x2 x3) (4ae4a.. 4a7ef..)),
x3.
Let x4 of type ι be given.
Let x5 of type ι be given.
Apply unknownprop_99ef3c56c8cdbdbdd0c30f3ff13386c5db4ed206a6215787f09bd20975ed1342 with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 : ο . iff (x2 x4 x5) x6 leaving 3 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying iff_refl with x2 x4 x5.