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Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι → ι be given.
Let x3 of type ι → ι → ι 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.
Claim L2: x0 = x1
Apply L1 with λ x10 x11 . x0 = x11.
The subproof is completed by applying unknownprop_ad9008b6f2810a0e7af71389371f7ebb2072060b97071ea08eac6648b1392012 with x0, x2, x4, x6, x8.
Apply and5I with x0 = x1, ∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x2 x10 x11 = x3 x10 x11, ∀ 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 be given.
Let x11 of type ι be given.
Apply unknownprop_68a0f865e52b1f2086cf38474b5b6a79876dd054c0b1d3fd70ebad35e03e9edb with x0, x2, x4, x6, x8, x10, x11, λ x12 x13 . x13 = x3 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 . e3162.. (f482f.. x13 (4ae4a.. 4a7ef..)) x10 x11 = x3 x10 x11.
Let x12 of type ι → ι → ο be given.
Apply unknownprop_68a0f865e52b1f2086cf38474b5b6a79876dd054c0b1d3fd70ebad35e03e9edb with x1, x3, x5, x7, x9, x10, x11, λ x13 x14 . 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.
Let x11 of type ι be given.
Apply unknownprop_903218825c8191e8fbd41c581818c0ede6ad6eef9ed65f1a49cd074f0c204395 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_903218825c8191e8fbd41c581818c0ede6ad6eef9ed65f1a49cd074f0c204395 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_cfa405b88b73d28820f49d9bf44e58432ec35b7af75bdb9faca7a7821189bcd7 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_cfa405b88b73d28820f49d9bf44e58432ec35b7af75bdb9faca7a7821189bcd7 with x1, x3, x5, x7, x9, x10, λ x12 x13 : ο . x11 x13 x12.
The subproof is completed by applying L4.
Apply unknownprop_cbf73d6429ec8fb960c667c86ebf36a6e504cfb29f13f37b32891904f10afd24 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_cbf73d6429ec8fb960c667c86ebf36a6e504cfb29f13f37b32891904f10afd24 with x1, x3, x5, x7, x9, λ x11 x12 . x10 x12 x11.
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