Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι → ο be given.
Let x4 of type ι → ο be given.
Let x5 of type ι → ο be given.
Assume H5:
PNoLt x0 x3 x1 x4.
Assume H6:
PNoLt x1 x4 x2 x5.
Apply unknownprop_7d798c5794ed96c61cc9ec828963a5831eee43021e8f1ea48be05a5cb53904e0 with
x0,
x1,
x3,
x4,
PNoLt x0 x3 x2 x5 leaving 4 subgoals.
The subproof is completed by applying H5.
Apply unknownprop_ff2db5d7cd089ead6d3f23ab1904a643f023d611ddbe42c5c85e87e080e26158 with
binintersect x0 x1,
x3,
x4,
PNoLt x0 x3 x2 x5 leaving 2 subgoals.
The subproof is completed by applying H7.
Let x6 of type ι be given.
Apply unknownprop_9f9c1680d203bdbb862d1bf6c2b8504d7e3a6fca72f77bd8968e86ad6ad69346 with
x0,
x1,
x6,
PNoEq_ x6 x3 x4 ⟶ not (x3 x6) ⟶ x4 x6 ⟶ PNoLt x0 x3 x2 x5 leaving 2 subgoals.
The subproof is completed by applying H8.
Assume H13: x4 x6.
Apply unknownprop_7d798c5794ed96c61cc9ec828963a5831eee43021e8f1ea48be05a5cb53904e0 with
x1,
x2,
x4,
x5,
PNoLt x0 x3 x2 x5 leaving 4 subgoals.
The subproof is completed by applying H6.
Apply unknownprop_ff2db5d7cd089ead6d3f23ab1904a643f023d611ddbe42c5c85e87e080e26158 with
binintersect x1 x2,
x4,
x5,
PNoLt x0 x3 x2 x5 leaving 2 subgoals.
The subproof is completed by applying H16.
Let x7 of type ι be given.
Apply unknownprop_9f9c1680d203bdbb862d1bf6c2b8504d7e3a6fca72f77bd8968e86ad6ad69346 with
x1,
x2,
x7,
PNoEq_ x7 x4 x5 ⟶ not (x4 x7) ⟶ x5 x7 ⟶ PNoLt x0 x3 x2 x5 leaving 2 subgoals.
The subproof is completed by applying H17.
Assume H22: x5 x7.
Apply unknownprop_2a38d5561acb46bf4581f375c3fb301a06d08a93dee7d2c06138bdaa38452584 with
x0,
x2,
x3,
x5.
Apply unknownprop_d3eaeaf2c92929364f7d313ca2b01dbaa8e7169d84112bc61a6ed9c6cb0d624a with
λ x8 x9 : ι → (ι → ο) → (ι → ο) → ο . x9 (binintersect x0 x2) x3 x5.
Apply unknownprop_497ef0b809178e9ac674acf0f41f994a7e76b824de0430efd934f6540a71daab with
x6,
x7,
∃ x8 . and (In x8 (binintersect x0 x2)) (and (and (PNoEq_ x8 x3 x5) (not (x3 x8))) (x5 x8)) leaving 5 subgoals.
The subproof is completed by applying L14.
The subproof is completed by applying L23.
Let x8 of type ο be given.
Apply H26 with
x6.
Apply unknownprop_389e2fb1855352fcc964ea44fe6723d7a1c2d512f04685300e3e97621725b977 with
In x6 (binintersect x0 x2),
and (and (PNoEq_ x6 x3 x5) (not (x3 x6))) (x5 x6) leaving 2 subgoals.
Apply unknownprop_7e73699eda4c2a35af8db1aea1ddace7d2346405cd3944ace259823e1ec33cf3 with
x0,
x2,
x6 leaving 2 subgoals.
The subproof is completed by applying H9.
Apply L4 with
x7,
x6 leaving 2 subgoals.
The subproof is completed by applying H19.
The subproof is completed by applying H25.
Apply unknownprop_c7bf67064987d41cefc55afb6af6ecbbb6b830405f2005e0def6e504b3ca3bf3 with
PNoEq_ x6 x3 x5,
not (x3 x6),
x5 x6 leaving 3 subgoals.
Apply unknownprop_e0f34743af27a604447ff8f709ee0ab4cfc998bf21a330579a3abf15b483f3e6 with
x6,
x3,
x4,
x5 leaving 2 subgoals.
The subproof is completed by applying H11.
Apply unknownprop_385a349774bd141f67c9640b600008e8534ed0c05d891557fd37870b1d687d7f with
x4,
x5,
x7,
x6 leaving 3 subgoals.
The subproof is completed by applying L23.
The subproof is completed by applying H25.
The subproof is completed by applying H20.
The subproof is completed by applying H12.
Apply unknownprop_d4c6f9663742385071dd283da85a9397dc2dfd0eede50c9fd289b7b23ca97cdd with
x4 x6,
x5 x6 leaving 2 subgoals.
Apply L24 with
x6.
The subproof is completed by applying H25.
The subproof is completed by applying H13.
Assume H25: x6 = x7.
Let x8 of type ο be given.
Assume H26:
∀ x9 . and ... ... ⟶ x8.