Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι → ο be given.
Let x3 of type ι → ι → ο be given.
Let x4 of type ι → ι → ο be given.
Let x5 of type ι → ι → ο be given.
Let x6 of type ι be given.
Let x7 of type ι be given.
Apply unknownprop_3daee33de52d85c4f80ae1c73177b80eb259b7d8103b516cb7fa83e575eef3c2 with
1f7e2.. 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_8056a838da97a86ae4b45f5a668b09b5d54224cecafdbbaa522039cdb61cdb64 with x0, x2, x4, x6.
Apply and4I with
x0 = x1,
∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x2 x8 x9 = x3 x8 x9,
∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x4 x8 x9 = x5 x8 x9,
x6 = x7 leaving 4 subgoals.
The subproof is completed by applying L2.
Let x8 of type ι be given.
Let x9 of type ι be given.
Apply unknownprop_3f14843b058ef468d228782d60bdfe824732271ba3964c94fe353c4c4bb3c45f with
x0,
x2,
x4,
x6,
x8,
x9,
λ x10 x11 : ο . x11 = x3 x8 x9 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply L2 with
λ x10 x11 . prim1 x8 x10.
The subproof is completed by applying H3.
Apply L2 with
λ x10 x11 . prim1 x9 x10.
The subproof is completed by applying H4.
Apply H0 with
λ x10 x11 . 2b2e3.. (f482f.. x11 (4ae4a.. 4a7ef..)) x8 x9 = x3 x8 x9.
Let x10 of type ο → ο → ο be given.
Apply unknownprop_3f14843b058ef468d228782d60bdfe824732271ba3964c94fe353c4c4bb3c45f with
x1,
x3,
x5,
x7,
x8,
x9,
λ x11 x12 : ο . x10 x12 x11 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L6.
Let x8 of type ι be given.
Let x9 of type ι be given.
Apply unknownprop_3ca258265efc0e5d7f9f9d52b4cbf8cbed02ce8da796a40e7191176f764deac7 with
x0,
x2,
x4,
x6,
x8,
x9,
λ x10 x11 : ο . x11 = x5 x8 x9 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply L2 with
λ x10 x11 . prim1 x8 x10.
The subproof is completed by applying H3.
Apply L2 with
λ x10 x11 . prim1 x9 x10.
The subproof is completed by applying H4.
Apply H0 with
λ x10 x11 . 2b2e3.. (f482f.. x11 (4ae4a.. (4ae4a.. 4a7ef..))) x8 x9 = x5 x8 x9.
Let x10 of type ο → ο → ο be given.
Apply unknownprop_3ca258265efc0e5d7f9f9d52b4cbf8cbed02ce8da796a40e7191176f764deac7 with
x1,
x3,
x5,
x7,
x8,
x9,
λ x11 x12 : ο . x10 x12 x11 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L6.
Apply unknownprop_b3efaa7975234558158f68aac4cbf88f3abd88ebde8cabe34c292cbf4d1900ee 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_b3efaa7975234558158f68aac4cbf88f3abd88ebde8cabe34c292cbf4d1900ee with x1, x3, x5, x7, λ x9 x10 . x8 x10 x9.