Let x0 of type ι be given.
Let x1 of type ι be given.
Apply unknownprop_85336ee07ace71a942dc508d3b8c851d9d6bb88511443b7dafbf11b71c263f4d with
λ x2 . 14149.. x0 (616bf.. x1 x2) = 616bf.. (14149.. x0 x1) (14149.. x0 x2) leaving 2 subgoals.
Apply unknownprop_0d2e8618ea244d22f7cc913b00fa77b277d9ba7cc6a18877e00000ded7fa2c79 with
x1,
λ x2 x3 . 14149.. x0 x3 = 616bf.. (14149.. x0 x1) (14149.. x0 4a7ef..).
Apply unknownprop_63d5ed0b5d3b2a9a063f903e166c6263ce12fd6bf7f7fd37a0e3fe7d20466f91 with
x0,
λ x2 x3 . 14149.. x0 x1 = 616bf.. (14149.. x0 x1) x3.
Let x2 of type ι → ι → ο be given.
The subproof is completed by applying unknownprop_0d2e8618ea244d22f7cc913b00fa77b277d9ba7cc6a18877e00000ded7fa2c79 with
14149.. x0 x1,
λ x3 x4 . x2 x4 x3.
Let x2 of type ι be given.
Apply unknownprop_52ad2c641f06ccb05422449032c6daa178243ae05b1152998946ffec9f2dc331 with
x1,
x2,
λ x3 x4 . 14149.. x0 x4 = 616bf.. (14149.. x0 x1) (14149.. x0 (4ae4a.. x2)) leaving 2 subgoals.
The subproof is completed by applying H2.
Apply unknownprop_df1b2baf102ee12829b37c01f19bfac87840dc98b8bed43c98e8486d3941b705 with
x0,
616bf.. x1 x2,
λ x3 x4 . x4 = 616bf.. (14149.. x0 x1) (14149.. x0 (4ae4a.. x2)) 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 . 616bf.. x0 x4 = 616bf.. (14149.. x0 x1) (14149.. x0 (4ae4a.. x2)).
Apply unknownprop_df1b2baf102ee12829b37c01f19bfac87840dc98b8bed43c98e8486d3941b705 with
x0,
x2,
λ x3 x4 . 616bf.. x0 (616bf.. (14149.. x0 x1) (14149.. x0 x2)) = 616bf.. (14149.. x0 x1) x4 leaving 2 subgoals.
The subproof is completed by applying H2.
Apply unknownprop_b792ceb66f60a6c096ad7552c141059f1f38cd4a5967b04d890745072b457b9f with
x0,
14149.. x0 x1,
14149.. x0 x2,
λ x3 x4 . x3 = 616bf.. (14149.. x0 x1) (616bf.. x0 (14149.. x0 x2)) leaving 4 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_a6b90744dda0953f61ea6db040f1ab51cb32b8fa53742e60c6b6833df8b67618 with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply unknownprop_a6b90744dda0953f61ea6db040f1ab51cb32b8fa53742e60c6b6833df8b67618 with
x0,
x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
Apply unknownprop_aa168b4c293425c2abd45282f70c213c6b1470480d07539c9debf1ff08466a37 with
x0,
14149.. x0 x1,
λ x3 x4 . 616bf.. x4 (14149.. x0 x2) = 616bf.. (14149.. x0 x1) (616bf.. x0 (14149.. x0 x2)) leaving 3 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_a6b90744dda0953f61ea6db040f1ab51cb32b8fa53742e60c6b6833df8b67618 with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply unknownprop_b792ceb66f60a6c096ad7552c141059f1f38cd4a5967b04d890745072b457b9f with
14149.. x0 x1,
x0,
14149.. x0 x2 leaving 3 subgoals.
Apply unknownprop_a6b90744dda0953f61ea6db040f1ab51cb32b8fa53742e60c6b6833df8b67618 with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
Apply unknownprop_a6b90744dda0953f61ea6db040f1ab51cb32b8fa53742e60c6b6833df8b67618 with
x0,
x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.