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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 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_8815c9f2cb5c52ada14e760a78176b23a29e95e0bce81e0ffdef5b9a742dfbb0 with 50941.. 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_4d3b1552f811436b8f29af8fa2db6a6f0ed851417fe4ea754fadac215fbbceef 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, x6 = x7, 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_1577ea96652eddec718222b40e2ddf7792be06e6a335faa6da4659776d8b2b7f 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_1577ea96652eddec718222b40e2ddf7792be06e6a335faa6da4659776d8b2b7f 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_303a5dcd96ccd0795a0c1c2f0ababef222f2dd40fc6be62386d34762cfdb65c5 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_303a5dcd96ccd0795a0c1c2f0ababef222f2dd40fc6be62386d34762cfdb65c5 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.
Apply unknownprop_ddb82a3c52c030568b927ce40224fa285ba790e62b2413b7fca117d1b06927bc 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_ddb82a3c52c030568b927ce40224fa285ba790e62b2413b7fca117d1b06927bc with x1, x3, x5, x7, x9, λ x11 x12 . x10 x12 x11.
Apply unknownprop_a2784db0fbde3c5924110ee44b88db7f7be64c189a40d459e45f4debf5b5aa45 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_a2784db0fbde3c5924110ee44b88db7f7be64c189a40d459e45f4debf5b5aa45 with x1, x3, x5, x7, x9, λ x11 x12 . x10 x12 x11.
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