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 be given.
Apply unknownprop_161e87a7ffc89f3ddd1785adde005689375fc50ffc9e69bd2228b35ea96e4960 with
11e73.. x0 x2,
x1,
x3.
The subproof is completed by applying H0.
Claim L2: x0 = x1
Apply L1 with
λ x4 x5 . x0 = x5.
The subproof is completed by applying unknownprop_34f20b60ad6d2956b7a8470b3a7eb1f27be254c9d3b55cfa21302e6ea7eed305 with x0, x2.
Apply andI with
x0 = x1,
x2 = x3 leaving 2 subgoals.
The subproof is completed by applying L2.
Apply unknownprop_c21db9eeb1cd5feb3cc621de0ea32fdccd69e665404c76a1b527a4c87e56a838 with
x0,
x2,
λ x4 x5 . x5 = x3.
Apply H0 with
λ x4 x5 . f482f.. x5 (4ae4a.. 4a7ef..) = x3.
Let x4 of type ι → ι → ο be given.
The subproof is completed by applying unknownprop_c21db9eeb1cd5feb3cc621de0ea32fdccd69e665404c76a1b527a4c87e56a838 with x1, x3, λ x5 x6 . x4 x6 x5.