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.
Apply unknownprop_8f17af3000c47bda68f7892969ccfe825272a56e510c58c98d268cf47566f2c8 with
942b6.. 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_d0c6645deb4e4a12bb2d204629b8d932c7c9885969a4f1b009b789ca36525db2 with x0, x2, x4, x6.
Apply and4I with
x0 = x1,
∀ x8 . prim1 x8 x0 ⟶ x2 x8 = x3 x8,
∀ x8 . prim1 x8 x0 ⟶ x4 x8 = x5 x8,
∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x6 x8 x9 = x7 x8 x9 leaving 4 subgoals.
The subproof is completed by applying L2.
Let x8 of type ι be given.
Apply unknownprop_c2318c3dd65accea00dadff6d47933b4587e236518978f4378818dcb690ba2d2 with
x0,
x2,
x4,
x6,
x8,
λ x9 x10 . x10 = x3 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.. 4a7ef..)) x8 = x3 x8.
Let x9 of type ι → ι → ο be given.
Apply unknownprop_c2318c3dd65accea00dadff6d47933b4587e236518978f4378818dcb690ba2d2 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_707e1d17e1b6b9966d50c66b71426f61a607a2737b77d1bc99065964130a4803 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_707e1d17e1b6b9966d50c66b71426f61a607a2737b77d1bc99065964130a4803 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.
Let x9 of type ι be given.
Apply unknownprop_55e99137b7e579558f9997426e99fef7b5d8724c4376472bfc9654d8923b03ef with
x0,
x2,
x4,
x6,
x8,
x9,
λ x10 x11 : ο . x11 = x7 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 . 2b2e3.. (f482f.. x11 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x8 x9 = x7 x8 x9.
Let x10 of type ο → ο → ο be given.
Apply unknownprop_55e99137b7e579558f9997426e99fef7b5d8724c4376472bfc9654d8923b03ef with
x1,
x3,
x5,
x7,
x8,
x9,
λ x11 x12 : ο . x10 x12 x11 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L6.