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 → ο be given.
Let x5 of type ι → ο be given.
Let x6 of type ι be given.
Let x7 of type ι be given.
Apply unknownprop_586382e0e1f10699a16172087564e088031f709c45fca919f123c5e504aa6455 with
c42e1.. 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_b585ddd2d1f87e91de57052e16fa9fc9f7f1c8519d74bb4e06810b6ca053a11d 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_683bfcbe4bb37f8c2f4fa117c5308204038b13f46c0af4ff7943cad8646fcf56 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_683bfcbe4bb37f8c2f4fa117c5308204038b13f46c0af4ff7943cad8646fcf56 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_2eb06be09378db168b599d1160cfb8b63718d4184d83ea92ee29734845bee9b8 with
x0,
x2,
x4,
x6,
x8,
λ x9 x10 : ο . 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 . decode_p (f482f.. x10 (4ae4a.. (4ae4a.. 4a7ef..))) x8 = x5 x8.
Let x9 of type ο → ο → ο be given.
Apply unknownprop_2eb06be09378db168b599d1160cfb8b63718d4184d83ea92ee29734845bee9b8 with
x1,
x3,
x5,
x7,
x8,
λ x10 x11 : ο . x9 x11 x10.
The subproof is completed by applying L4.
Apply unknownprop_469b03203711fed4c87fd71fa2d6c39cf5b64ad461f7d8704fa32e6ec790e785 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_469b03203711fed4c87fd71fa2d6c39cf5b64ad461f7d8704fa32e6ec790e785 with x1, x3, x5, x7, λ x9 x10 . x8 x10 x9.