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 be given.
Let x7 of type ι be given.
Apply unknownprop_1f7335024129a3da23783a3ac07615a7380934700ab267b3c40b83bdc7d6705a with
eb2d9.. 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_764acd696e647f6c1e13399f20c3d7a0c3012dbddcc1f8ac4bfc81ffd50a5120 with x0, x2, x4, x6.
Apply and4I with
x0 = x1,
∀ x8 : ι → ο . (∀ x9 . x8 x9 ⟶ prim1 x9 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 → ο be given.
Assume H3:
∀ x9 . x8 x9 ⟶ prim1 x9 x0.
Apply unknownprop_52bd681fb48f0194a26e56d7979f5439861b31be106e42108fdfa19b563fc551 with
x0,
x2,
x4,
x6,
x8,
λ x9 x10 : ο . x10 = x3 x8 leaving 2 subgoals.
The subproof is completed by applying H3.
Claim L4:
∀ x9 . x8 x9 ⟶ prim1 x9 x1Apply L2 with
λ x9 x10 . ∀ x11 . x8 x11 ⟶ prim1 x11 x9.
The subproof is completed by applying H3.
Apply H0 with
λ x9 x10 . decode_c (f482f.. x10 (4ae4a.. 4a7ef..)) x8 = x3 x8.
Let x9 of type ο → ο → ο be given.
Apply unknownprop_52bd681fb48f0194a26e56d7979f5439861b31be106e42108fdfa19b563fc551 with
x1,
x3,
x5,
x7,
x8,
λ x10 x11 : ο . x9 x11 x10.
The subproof is completed by applying L4.
Let x8 of type ι be given.
Apply unknownprop_4712bc13b5160d975333d7566668b80deb133d8f8a6b96429e546b412c5a3772 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_4712bc13b5160d975333d7566668b80deb133d8f8a6b96429e546b412c5a3772 with
x1,
x3,
x5,
x7,
x8,
λ x10 x11 . x9 x11 x10.
The subproof is completed by applying L4.
Apply unknownprop_1524b180c69719302ec1be9fcae9d9a2668e7c2c94321e7b5052dbf5ecee2166 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_1524b180c69719302ec1be9fcae9d9a2668e7c2c94321e7b5052dbf5ecee2166 with x1, x3, x5, x7, λ x9 x10 . x8 x10 x9.