Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι → ι be given.
Let x3 of type ι → ι → ι be given.
Let x4 of type ι be given.
Let x5 of type ι be given.
Apply unknownprop_b8fca82ae3bd1ab42ec0b368c1d6f5c65c1d050470d779be27ba83e98b2e3ea8 with
96158.. 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_3bd6f6e5afa239de2bed4c5d0a7e768286a329bd2689d74ed28c7c62d231db6f with x0, x2, x4.
Apply and3I with
x0 = x1,
∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x2 x6 x7 = x3 x6 x7,
x4 = x5 leaving 3 subgoals.
The subproof is completed by applying L2.
Let x6 of type ι be given.
Let x7 of type ι be given.
Apply unknownprop_aec86eb4da68e7f79235ce435d2568a1f89bad923e23fefb04b9885bd4542138 with
x0,
x2,
x4,
x6,
x7,
λ x8 x9 . x9 = x3 x6 x7 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply L2 with
λ x8 x9 . prim1 x6 x8.
The subproof is completed by applying H3.
Apply L2 with
λ x8 x9 . prim1 x7 x8.
The subproof is completed by applying H4.
Apply H0 with
λ x8 x9 . e3162.. (f482f.. x9 (4ae4a.. 4a7ef..)) x6 x7 = x3 x6 x7.
Let x8 of type ι → ι → ο be given.
Apply unknownprop_aec86eb4da68e7f79235ce435d2568a1f89bad923e23fefb04b9885bd4542138 with
x1,
x3,
x5,
x6,
x7,
λ x9 x10 . x8 x10 x9 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L6.
Apply unknownprop_22fa583cdd675dc491864c4bc88d6afb2cb2c5c899f3088bafeb1dd37fbf3527 with
x0,
x2,
x4,
λ x6 x7 . x7 = x5.
Apply H0 with
λ x6 x7 . f482f.. x7 (4ae4a.. (4ae4a.. 4a7ef..)) = x5.
Let x6 of type ι → ι → ο be given.
The subproof is completed by applying unknownprop_22fa583cdd675dc491864c4bc88d6afb2cb2c5c899f3088bafeb1dd37fbf3527 with x1, x3, x5, λ x7 x8 . x6 x8 x7.