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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 → 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 → ο be given.
Let x9 of type ι → ο be given.
Claim L2: x0 = x1
Apply L1 with λ x10 x11 . x0 = x11.
The subproof is completed by applying unknownprop_9b935f184e6ef19fd2887b24efdd6195f442b8ceca35e964096d01e16d81456d with x0, x2, x4, ..., ....
Apply and5I with x0 = x1, ∀ x10 . prim1 x10 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, ∀ x10 . prim1 x10 x0 ⟶ x8 x10 = x9 x10 leaving 5 subgoals.
The subproof is completed by applying L2.
Let x10 of type ι be given.
Apply unknownprop_33b004c8f62843bcba581c3bb62c1b6860ed0922825af08a3ae7ea18e3233657 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_33b004c8f62843bcba581c3bb62c1b6860ed0922825af08a3ae7ea18e3233657 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_cc298fd33dfe686ee7b576905469258d62cae8b4852e26a02f0aa0c50d1f2c8b 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_cc298fd33dfe686ee7b576905469258d62cae8b4852e26a02f0aa0c50d1f2c8b 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_4d5576adce78b831f45c33ebbe5605fa8b4e2b873b249b058e32db9cb78c1ede 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_4d5576adce78b831f45c33ebbe5605fa8b4e2b873b249b058e32db9cb78c1ede 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_83e4e93ebfb84f8cd49bab263850d2028f52dcb8263fa261f8e447c5e6ace519 with x0, x2, x4, x6, x8, x10, λ x11 x12 : ο . x12 = x9 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.. (4ae4a.. 4a7ef..))))) x10 = x9 x10.
Let x11 of type ο → ο → ο be given.
Apply unknownprop_83e4e93ebfb84f8cd49bab263850d2028f52dcb8263fa261f8e447c5e6ace519 with x1, x3, x5, x7, x9, x10, λ x12 x13 : ο . x11 x13 x12.
The subproof is completed by applying L4.
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