Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ο 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.
Let x6 of type ι be given.
Let x7 of type ι be given.
Apply unknownprop_ad831e61ed7a994f655af9741f7231d9dadba8b18b17c6d06e537094201fddf2 with
9a89f.. x0 x2 x4 x6,
x1,
x3,
x5,
x7.
The subproof is completed by applying H0.
Claim L2: x0 = x1
Apply L1 with
λ x8 x9 . x0 = x9.
The subproof is completed by applying unknownprop_a576ff427cd318768867456a602be7385ebe63dbd963b27f10917adc75dc8282 with x0, x2, x4, x6.
Apply and4I with
x0 = x1,
∀ x8 . prim1 x8 x0 ⟶ x2 x8 = x3 x8,
∀ x8 . prim1 x8 x0 ⟶ x4 x8 = x5 x8,
x6 = x7 leaving 4 subgoals.
The subproof is completed by applying L2.
Let x8 of type ι be given.
Apply unknownprop_4548e98d35c6fb7e16df7a33511bfb2db06dacdf7d2ed47cd75df680654af064 with
x0,
x2,
x4,
x6,
x8,
λ x9 x10 : ο . x10 = x3 x8 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply L2 with
λ x9 x10 . prim1 x8 x9.
The subproof is completed by applying H3.
Apply H0 with
λ x9 x10 . decode_p (f482f.. x10 (4ae4a.. 4a7ef..)) x8 = x3 x8.
Let x9 of type ο → ο → ο be given.
Apply unknownprop_4548e98d35c6fb7e16df7a33511bfb2db06dacdf7d2ed47cd75df680654af064 with
x1,
x3,
x5,
x7,
x8,
λ x10 x11 : ο . x9 x11 x10.
The subproof is completed by applying L4.
Let x8 of type ι be given.
Apply unknownprop_993bd80091dd1d96989c6f7e5192d0c5e7c03a63fa9eb1a1dcfc0ffe8d54833d with
x0,
x2,
x4,
x6,
x8,
λ x9 x10 : ο . x10 = x5 x8 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply L2 with
λ x9 x10 . prim1 x8 x9.
The subproof is completed by applying H3.
Apply H0 with
λ x9 x10 . decode_p (f482f.. x10 (4ae4a.. (4ae4a.. 4a7ef..))) x8 = x5 x8.
Let x9 of type ο → ο → ο be given.
Apply unknownprop_993bd80091dd1d96989c6f7e5192d0c5e7c03a63fa9eb1a1dcfc0ffe8d54833d with
x1,
x3,
x5,
x7,
x8,
λ x10 x11 : ο . x9 x11 x10.
The subproof is completed by applying L4.
Apply unknownprop_192fd6bdb7e2fbd211637c744c2a289601fd6343dc99fbe58167f21d601083f0 with
x0,
x2,
x4,
x6,
λ x8 x9 . x9 = x7.
Apply H0 with
λ x8 x9 . f482f.. x9 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) = x7.
Let x8 of type ι → ι → ο be given.
The subproof is completed by applying unknownprop_192fd6bdb7e2fbd211637c744c2a289601fd6343dc99fbe58167f21d601083f0 with x1, x3, x5, x7, λ x9 x10 . x8 x10 x9.