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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 be given.
Let x5 of type ι → ι be given.
Let x6 of type ι → ι → ο be given.
Let x7 of type ι → ι → ο be given.
Let x8 of type ι be given.
Let x9 of type ι be given.
Apply unknownprop_926f5dead26fa3fbf47fa88ba3d8e016f7b3ce528fc67b1ec0b1acfc2e17c80a with 608f4.. x0 ... ... ... ..., ..., ..., ..., ..., ....
Claim L2: x0 = x1
Apply L1 with λ x10 x11 . x0 = x11.
The subproof is completed by applying unknownprop_76b5a9af532ac0913e28c26dcb52f8b5abf00c237ad1183ccb34561534e54b58 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 ⟶ x4 x10 = x5 x10, ∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x6 x10 x11 = x7 x10 x11, 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_e7fb1a23b56108a135d0d02f7d4bcc2d7fac955b5f6b4851e4790ea068dff520 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 x1Apply 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_e7fb1a23b56108a135d0d02f7d4bcc2d7fac955b5f6b4851e4790ea068dff520 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.
Apply unknownprop_df43306d77e4a4eb6f67f1d5f13b1d59fa448ea7b27eac12f811d767a7e34eb9 with x0, x2, x4, x6, x8, x10, λ x11 x12 . 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 . f482f.. (f482f.. x12 (4ae4a.. (4ae4a.. 4a7ef..))) x10 = x5 x10.
Let x11 of type ι → ι → ο be given.
Apply unknownprop_df43306d77e4a4eb6f67f1d5f13b1d59fa448ea7b27eac12f811d767a7e34eb9 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.
Let x11 of type ι be given.
Apply unknownprop_c2dfa7ef43af28df5b4a6c6bad505fe4501bc22df791f124eb4670f1ad596748 with x0, x2, x4, x6, x8, x10, x11, λ x12 x13 : ο . x13 = x7 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.. (4ae4a.. 4a7ef..)))) x10 x11 = x7 x10 x11.
Let x12 of type ο → ο → ο be given.
Apply unknownprop_c2dfa7ef43af28df5b4a6c6bad505fe4501bc22df791f124eb4670f1ad596748 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_514c1b4652039303e55e8ff6867562dea04990deb94b97d805e15cc0e4901456 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_514c1b4652039303e55e8ff6867562dea04990deb94b97d805e15cc0e4901456 with x1, x3, x5, x7, x9, λ x11 x12 . x10 x12 x11.
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