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Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type (ι → ο) → ο be given.
Let x3 of type (ι → ο) → ο be given.
Let x4 of type ι → ι → ο be given.
Let x5 of type ι → ι → ο be given.
Let x6 of type ι → ο be given.
Let x7 of type ι → ο be given.
Let x8 of type ι be given.
Let x9 of type ι be given.
Apply unknownprop_5dace1e87a84357530b97ff9ad3bd9b43b92295b7638cf3c2712453650299ce8 with a3459.. x0 ... ... ... ..., ..., ..., ..., ..., ....
Claim L2: x0 = x1
Apply L1 with λ x10 x11 . x0 = x11.
The subproof is completed by applying unknownprop_97c6febb4d48ff36e4cb1a67ae96e731bb4d0d88ae631b336ee8d751a8ea3644 with x0, x2, x4, x6, x8.
Apply and5I with x0 = x1, ∀ x10 : ι → ο . (∀ x11 . x10 x11 ⟶ prim1 x11 x0) ⟶ x2 x10 = x3 x10, ∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x4 x10 x11 = x5 x10 x11, ∀ x10 . prim1 x10 x0 ⟶ x6 x10 = x7 x10, x8 = x9 leaving 5 subgoals.
The subproof is completed by applying L2.
Let x10 of type ι → ο be given.
Assume H3: ∀ x11 . x10 x11 ⟶ prim1 x11 x0.
Apply unknownprop_f126e736effd1cf0374523a6b7386d5add53fdd920a5f78d4f4f605963832861 with x0, x2, x4, x6, x8, x10, λ x11 x12 : ο . x12 = x3 x10 leaving 2 subgoals.
The subproof is completed by applying H3.
Claim L4: ∀ x11 . x10 x11 ⟶ prim1 x11 x1
Apply L2 with λ x11 x12 . ∀ x13 . x10 x13 ⟶ prim1 x13 x11.
The subproof is completed by applying H3.
Apply H0 with λ x11 x12 . decode_c (f482f.. x12 (4ae4a.. 4a7ef..)) x10 = x3 x10.
Let x11 of type ο → ο → ο be given.
Apply unknownprop_f126e736effd1cf0374523a6b7386d5add53fdd920a5f78d4f4f605963832861 with x1, x3, x5, x7, x9, x10, λ x12 x13 : ο . x11 x13 x12.
The subproof is completed by applying L4.
Let x10 of type ι be given.
Let x11 of type ι be given.
Apply unknownprop_3b64a3196710182a4d35cba1546eee2e2f7980f2ed75b429503d9f04f3d32e71 with x0, x2, x4, x6, x8, x10, x11, λ x12 x13 : ο . x13 = x5 x10 x11 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply L2 with λ x12 x13 . prim1 x10 x12.
The subproof is completed by applying H3.
Apply L2 with λ x12 x13 . prim1 x11 x12.
The subproof is completed by applying H4.
Apply H0 with λ x12 x13 . 2b2e3.. (f482f.. x13 (4ae4a.. (4ae4a.. 4a7ef..))) x10 x11 = x5 x10 x11.
Let x12 of type ο → ο → ο be given.
Apply unknownprop_3b64a3196710182a4d35cba1546eee2e2f7980f2ed75b429503d9f04f3d32e71 with x1, x3, x5, x7, x9, x10, x11, λ x13 x14 : ο . x12 x14 x13 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L6.
Let x10 of type ι be given.
Apply unknownprop_a2cc32195c89ba000a0e2e102a49e880cf6082a249cefcf846a21241ed3c6cf3 with x0, x2, x4, x6, x8, x10, λ x11 x12 : ο . x12 = x7 x10 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply L2 with λ x11 x12 . prim1 x10 x11.
The subproof is completed by applying H3.
Apply H0 with λ x11 x12 . decode_p (f482f.. x12 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x10 = x7 x10.
Let x11 of type ο → ο → ο be given.
Apply unknownprop_a2cc32195c89ba000a0e2e102a49e880cf6082a249cefcf846a21241ed3c6cf3 with x1, x3, x5, x7, x9, x10, λ x12 x13 : ο . x11 x13 x12.
The subproof is completed by applying L4.
Apply unknownprop_68fa418e80e05b5f5d85946aaba333bbaea1a45e6bff44a3e7bbfdbb8602422f with x0, x2, x4, x6, x8, λ x10 x11 . x11 = x9.
Apply H0 with λ x10 x11 . f482f.. x11 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) = x9.
Let x10 of type ι → ι → ο be given.
The subproof is completed by applying unknownprop_68fa418e80e05b5f5d85946aaba333bbaea1a45e6bff44a3e7bbfdbb8602422f with x1, x3, x5, x7, x9, λ x11 x12 . x10 x12 x11.
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