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 andI with
x0 = x2,
x1 = x3 leaving 2 subgoals.
Apply unknownprop_7e986439242ce85fa04e4b7be2035418e9dbee6641ed66c6c5b7be52a2254fca with
x0,
x1,
λ x4 x5 . x4 = x2.
Apply unknownprop_7e986439242ce85fa04e4b7be2035418e9dbee6641ed66c6c5b7be52a2254fca with
x2,
x3,
λ x4 x5 . e76d4.. (aae7a.. x0 x1) = x4.
Apply H0 with
λ x4 x5 . e76d4.. x5 = e76d4.. (aae7a.. x2 x3).
Let x4 of type ι → ι → ο be given.
The subproof is completed by applying H1.
Apply unknownprop_916f469d850241375b1e44b2c6308f0113078869ceee129c02712fae69c32a37 with
x0,
x1,
λ x4 x5 . x4 = x3.
Apply unknownprop_916f469d850241375b1e44b2c6308f0113078869ceee129c02712fae69c32a37 with
x2,
x3,
λ x4 x5 . 22ca9.. (aae7a.. x0 x1) = x4.
Apply H0 with
λ x4 x5 . 22ca9.. x5 = 22ca9.. (aae7a.. x2 x3).
Let x4 of type ι → ι → ο be given.
The subproof is completed by applying H1.