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 be given.
Let x7 of type ι be given.
Apply unknownprop_860ef8aa77a7ae3d2d46999c9ef185eebbc09dd8a4461c8ad597663a40687f92 with
5f184.. 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_493364ac88238c997501142687588779e16101987e5073e40eae76097712d5dd 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,
x6 = x7 leaving 4 subgoals.
The subproof is completed by applying L2.
Let x8 of type ι be given.
Apply unknownprop_28402dcc2ba78e14087bcd961f8274ab7fa38430ac7a3b1854b0846cad4bc690 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_28402dcc2ba78e14087bcd961f8274ab7fa38430ac7a3b1854b0846cad4bc690 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_82f0f89ba777ffd2c4f25e9fdd4a8b721fe1265d0911aa185e88a98c4ee67cc8 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_82f0f89ba777ffd2c4f25e9fdd4a8b721fe1265d0911aa185e88a98c4ee67cc8 with
x1,
x3,
x5,
x7,
x8,
λ x10 x11 . x9 x11 x10.
The subproof is completed by applying L4.
Apply unknownprop_40771ea886f80f98b32d1d881282250648392acc12c645469c87344f1af7fc17 with
x0,
x2,
x4,
x6,
λ x8 x9 . x9 = x7.
Apply H0 with
λ x8 x9 . f482f.. x9 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) = x7.
Let x8 of type ι → ι → ο be given.
The subproof is completed by applying unknownprop_40771ea886f80f98b32d1d881282250648392acc12c645469c87344f1af7fc17 with x1, x3, x5, x7, λ x9 x10 . x8 x10 x9.