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.
Apply unknownprop_f3e9c55b476f54285bbdfa8ab89b23919535add488591b1a7699e49226b365d3 with
fc7e7.. x0 x2 x4,
x1,
x3,
x5.
The subproof is completed by applying H0.
Claim L2: x0 = x1
Apply L1 with
λ x6 x7 . x0 = x7.
The subproof is completed by applying unknownprop_02cad8e0186a13edac760a40b04d581d34236e30332ea33ec2471a5050e9b8b5 with x0, x2, x4.
Apply and3I with
x0 = x1,
∀ x6 : ι → ο . (∀ x7 . x6 x7 ⟶ prim1 x7 x0) ⟶ x2 x6 = x3 x6,
∀ x6 . prim1 x6 x0 ⟶ x4 x6 = x5 x6 leaving 3 subgoals.
The subproof is completed by applying L2.
Let x6 of type ι → ο be given.
Assume H3:
∀ x7 . x6 x7 ⟶ prim1 x7 x0.
Apply unknownprop_c0871275b39d34d2963c3a36a1dfeee6d52fc7b10ea038c0356ce70595fa5b0f with
x0,
x2,
x4,
x6,
λ x7 x8 : ο . x8 = x3 x6 leaving 2 subgoals.
The subproof is completed by applying H3.
Claim L4:
∀ x7 . x6 x7 ⟶ prim1 x7 x1Apply L2 with
λ x7 x8 . ∀ x9 . x6 x9 ⟶ prim1 x9 x7.
The subproof is completed by applying H3.
Apply H0 with
λ x7 x8 . decode_c (f482f.. x8 (4ae4a.. 4a7ef..)) x6 = x3 x6.
Let x7 of type ο → ο → ο be given.
Apply unknownprop_c0871275b39d34d2963c3a36a1dfeee6d52fc7b10ea038c0356ce70595fa5b0f with
x1,
x3,
x5,
x6,
λ x8 x9 : ο . x7 x9 x8.
The subproof is completed by applying L4.
Let x6 of type ι be given.
Apply unknownprop_d032a8bd5d30b0278d4b4eaea55e89ad39f6273a17060935741b85f1e05b0ccf with
x0,
x2,
x4,
x6,
λ x7 x8 . x8 = x5 x6 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply L2 with
λ x7 x8 . prim1 x6 x7.
The subproof is completed by applying H3.
Apply H0 with
λ x7 x8 . f482f.. (f482f.. x8 (4ae4a.. (4ae4a.. 4a7ef..))) x6 = x5 x6.
Let x7 of type ι → ι → ο be given.
Apply unknownprop_d032a8bd5d30b0278d4b4eaea55e89ad39f6273a17060935741b85f1e05b0ccf with
x1,
x3,
x5,
x6,
λ x8 x9 . x7 x9 x8.
The subproof is completed by applying L4.