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Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι be given.
Let x3 of type ι → ι 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.
Let x8 of type ι be given.
Let x9 of type ι be given.
Apply unknownprop_851fa9d166936049dbe6d18ab505f5dbb48c6bd5f417095cf561aef422f437fa with 726e4.. x0 x2 x4 x6 x8, x1, x3, x5, x7, x9.
The subproof is completed by applying H0.
Claim L2: x0 = x1
Apply L1 with λ x10 x11 . x0 = x11.
The subproof is completed by applying unknownprop_f765175e49be2e5a6aa2dddd3f196b09de0d3db9e2abfd3e4e13e6768629fafe with x0, x2, x4, x6, x8.
Apply and5I with x0 = x1, ∀ x10 . prim1 x10 x0 ⟶ x2 x10 = x3 x10, ∀ x10 . prim1 x10 x0 ⟶ x4 x10 = x5 x10, x6 = x7, x8 = x9 leaving 5 subgoals.
The subproof is completed by applying L2.
Let x10 of type ι be given.
Apply unknownprop_e85ab008414ff526d780a8e87fe0b9a7f0f190685865daf112d41a71237f0351 with x0, x2, x4, x6, x8, x10, λ x11 x12 . x12 = x3 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 . f482f.. (f482f.. x12 (4ae4a.. 4a7ef..)) x10 = x3 x10.
Let x11 of type ι → ι → ο be given.
Apply unknownprop_e85ab008414ff526d780a8e87fe0b9a7f0f190685865daf112d41a71237f0351 with x1, x3, x5, x7, x9, x10, λ x12 x13 . x11 x13 x12.
The subproof is completed by applying L4.
Let x10 of type ι be given.
Apply unknownprop_b61615c9653894c6dfafd0ba94cef8f8845ac86458c933668ce3bd896e2d4a41 with x0, x2, x4, x6, x8, x10, λ x11 x12 : ο . x12 = x5 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.. 4a7ef..))) x10 = x5 x10.
Let x11 of type ο → ο → ο be given.
Apply unknownprop_b61615c9653894c6dfafd0ba94cef8f8845ac86458c933668ce3bd896e2d4a41 with x1, x3, x5, x7, x9, x10, λ x12 x13 : ο . x11 x13 x12.
The subproof is completed by applying L4.
Apply unknownprop_dcbb4c59274350f3f1d7187419c84249f504e8939c586146795768afcc9fb03f with x0, x2, x4, x6, x8, λ x10 x11 . x11 = x7.
Apply H0 with λ x10 x11 . f482f.. x11 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) = x7.
Let x10 of type ι → ι → ο be given.
The subproof is completed by applying unknownprop_dcbb4c59274350f3f1d7187419c84249f504e8939c586146795768afcc9fb03f with x1, x3, x5, x7, x9, λ x11 x12 . x10 x12 x11.
Apply unknownprop_2dccef3492650341a1b94804dbaa3d10f6307d1141b055c4c1e8d5afc270c4ed 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_2dccef3492650341a1b94804dbaa3d10f6307d1141b055c4c1e8d5afc270c4ed with x1, x3, x5, x7, x9, λ x11 x12 . x10 x12 x11.
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