Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = 971d3.. (f482f.. x1 4a7ef..) (e3162.. (f482f.. x1 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x1 (4ae4a.. (4ae4a.. 4a7ef..)))).
Let x1 of type ι be given.
Let x2 of type ι → ι → ι be given.
Let x3 of type ι → ι be given.
Apply unknownprop_0de249c9a6cc0d3bcd5cc89147ea799acb4f233823c55edb760ffe9d4ffc7a91 with
x1,
x2,
x3,
λ x4 x5 . 971d3.. x1 x2 x3 = 971d3.. x4 (e3162.. (f482f.. (971d3.. x1 x2 x3) (4ae4a.. 4a7ef..))) (f482f.. (f482f.. (971d3.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..)))).
Apply unknownprop_24266e9a959c8e6147137b1f15474e7cc23ac34fcc9d6ccbda83d08c6097a3de with
x1,
x2,
e3162.. (f482f.. (971d3.. x1 x2 x3) (4ae4a.. 4a7ef..)),
x3,
f482f.. (f482f.. (971d3.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) leaving 2 subgoals.
The subproof is completed by applying unknownprop_6a5674efb6b0d571fb24cd5f7a30b471eec1bdac0d350bb303a07726f30cd6bf with x1, x2, x3.
The subproof is completed by applying unknownprop_8107478b497c3b04aa44623f19e37dac344de98a93384327865b5df8b8117888 with x1, x2, x3.