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 be given.
Let x5 of type ι → ι be given.
Let x6 of type ι → ο be given.
Let x7 of type ι → ο be given.
Apply unknownprop_9be8536173b706235166955c9e469deb6842ecfdd57ba27e98cfdddc8af2a9df with
1670d.. x0 x2 x4 x6,
x1,
x3,
x5,
x7.
The subproof is completed by applying H0.
Claim L2: x0 = x1
Apply L1 with
λ x8 x9 . x0 = x9.
The subproof is completed by applying unknownprop_671251b916faa9f30bde4669a014519d7c43936df2d92d60762c27df7b65a3f5 with x0, x2, x4, x6.
Apply and4I with
x0 = x1,
∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x2 x8 x9 = x3 x8 x9,
∀ x8 . prim1 x8 x0 ⟶ x4 x8 = x5 x8,
∀ x8 . prim1 x8 x0 ⟶ x6 x8 = x7 x8 leaving 4 subgoals.
The subproof is completed by applying L2.
Let x8 of type ι be given.
Let x9 of type ι be given.
Apply unknownprop_201c00f4dc546c1c361481e6df2db6a0eaaed987dfc99dd72aafe0c44e14d85c with
x0,
x2,
x4,
x6,
x8,
x9,
λ x10 x11 . x11 = x3 x8 x9 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply L2 with
λ x10 x11 . prim1 x8 x10.
The subproof is completed by applying H3.
Apply L2 with
λ x10 x11 . prim1 x9 x10.
The subproof is completed by applying H4.
Apply H0 with
λ x10 x11 . e3162.. (f482f.. x11 (4ae4a.. 4a7ef..)) x8 x9 = x3 x8 x9.
Let x10 of type ι → ι → ο be given.
Apply unknownprop_201c00f4dc546c1c361481e6df2db6a0eaaed987dfc99dd72aafe0c44e14d85c with
x1,
x3,
x5,
x7,
x8,
x9,
λ x11 x12 . x10 x12 x11 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L6.
Let x8 of type ι be given.
Apply unknownprop_e22c9b8bbaf8c317cab2c404e4bfbf3bd3c6d0de5b90be91aa49bf9920fa5b22 with
x0,
x2,
x4,
x6,
x8,
λ x9 x10 . x10 = x5 x8 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply L2 with
λ x9 x10 . prim1 x8 x9.
The subproof is completed by applying H3.
Apply H0 with
λ x9 x10 . f482f.. (f482f.. x10 (4ae4a.. (4ae4a.. 4a7ef..))) x8 = x5 x8.
Let x9 of type ι → ι → ο be given.
Apply unknownprop_e22c9b8bbaf8c317cab2c404e4bfbf3bd3c6d0de5b90be91aa49bf9920fa5b22 with
x1,
x3,
x5,
x7,
x8,
λ x10 x11 . x9 x11 x10.
The subproof is completed by applying L4.
Let x8 of type ι be given.
Apply unknownprop_ec7e3e177a83a4e42d38d8856b0fff216c61fbfa7dac384f7cc308a89915b411 with
x0,
x2,
x4,
x6,
x8,
λ x9 x10 : ο . x10 = x7 x8 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply L2 with
λ x9 x10 . prim1 x8 x9.
The subproof is completed by applying H3.
Apply H0 with
λ x9 x10 . decode_p (f482f.. x10 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x8 = x7 x8.
Let x9 of type ο → ο → ο be given.
Apply unknownprop_ec7e3e177a83a4e42d38d8856b0fff216c61fbfa7dac384f7cc308a89915b411 with
x1,
x3,
x5,
x7,
x8,
λ x10 x11 : ο . x9 x11 x10.
The subproof is completed by applying L4.