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 → ο be given.
Let x7 of type ι → ο be given.
Apply unknownprop_f27d5468050e5c3ee6aadd94ddc43de73246f10397ea6df378a80b930eeed94e with
7ba51.. 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_de92d664051bae83454b194e690fca03a8272522f5ad5d042a8d91459880662d 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 ⟶ x6 x8 = x7 x8 leaving 4 subgoals.
The subproof is completed by applying L2.
Let x8 of type ι be given.
Apply unknownprop_872a556b6150b80f45b2d59f5ba6ad3e271d91f36748d2151b2959da9e1f2fee 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_872a556b6150b80f45b2d59f5ba6ad3e271d91f36748d2151b2959da9e1f2fee 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_74e84643bb95b0b603e98176f2e9987ba527acafe21e0b3b2868c9969f37eb5b 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_74e84643bb95b0b603e98176f2e9987ba527acafe21e0b3b2868c9969f37eb5b 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_2ff6fecd0198d6fdbd7de25cb9eef11591da871697969a2154ebf8ef906f88c2 with
x0,
x2,
x4,
x6,
x8,
λ x9 x10 : ο . x10 = x7 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.. (4ae4a.. 4a7ef..)))) x8 = x7 x8.
Let x9 of type ο → ο → ο be given.
Apply unknownprop_2ff6fecd0198d6fdbd7de25cb9eef11591da871697969a2154ebf8ef906f88c2 with
x1,
x3,
x5,
x7,
x8,
λ x10 x11 : ο . x9 x11 x10.
The subproof is completed by applying L4.