Let x0 of type ι be given.
Let x1 of type ι be given.
Apply unknownprop_85336ee07ace71a942dc508d3b8c851d9d6bb88511443b7dafbf11b71c263f4d with
λ x2 . 616bf.. (616bf.. x0 x1) x2 = 616bf.. x0 (616bf.. x1 x2) leaving 2 subgoals.
Apply unknownprop_0d2e8618ea244d22f7cc913b00fa77b277d9ba7cc6a18877e00000ded7fa2c79 with
616bf.. x0 x1,
λ x2 x3 . x3 = 616bf.. x0 (616bf.. x1 4a7ef..).
Apply unknownprop_0d2e8618ea244d22f7cc913b00fa77b277d9ba7cc6a18877e00000ded7fa2c79 with
x1,
λ x2 x3 . 616bf.. x0 x1 = 616bf.. x0 x3.
Let x2 of type ι → ι → ο be given.
The subproof is completed by applying H2.
Let x2 of type ι be given.
Apply unknownprop_52ad2c641f06ccb05422449032c6daa178243ae05b1152998946ffec9f2dc331 with
616bf.. x0 x1,
x2,
λ x3 x4 . x4 = 616bf.. x0 (616bf.. x1 (4ae4a.. x2)) leaving 2 subgoals.
The subproof is completed by applying H2.
Apply unknownprop_52ad2c641f06ccb05422449032c6daa178243ae05b1152998946ffec9f2dc331 with
x1,
x2,
λ x3 x4 . 4ae4a.. (616bf.. (616bf.. x0 x1) x2) = 616bf.. x0 x4 leaving 2 subgoals.
The subproof is completed by applying H2.
Apply unknownprop_52ad2c641f06ccb05422449032c6daa178243ae05b1152998946ffec9f2dc331 with
x0,
616bf.. x1 x2,
λ x3 x4 . 4ae4a.. (616bf.. (616bf.. x0 x1) x2) = x4 leaving 2 subgoals.
Apply unknownprop_6ea59642454c806d36d2cfe931420377c027fcaf6c044cc84fb5291b346de8a0 with
x1,
x2 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply H3 with
λ x3 x4 . 4ae4a.. x4 = 4ae4a.. (616bf.. x0 (616bf.. x1 x2)).
Let x3 of type ι → ι → ο be given.
The subproof is completed by applying H4.