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 → ι → ι be given.
Let x5 of type ι → ι → ι be given.
Let x6 of type ι be given.
Let x7 of type ι be given.
Apply unknownprop_d26df5fbd1232d69dce26e2d7ea1db72a097f7918e729051f5e26168a38b9ff6 with
e707a.. 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_7f8cf709626e3c3070e0159083b1ab8e788ca07cfe449c68d5a1358d4ee66821 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_64706c046583f0aebfd798d86fb2bddc5986f4bf9579571a82843d1c7a79f3bb with
x0,
x2,
x4,
x6,
x8,
x9,
λ x10 x11 . 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 . e3162.. (f482f.. x11 (4ae4a.. 4a7ef..)) x8 x9 = x3 x8 x9.
Let x10 of type ι → ι → ο be given.
Apply unknownprop_64706c046583f0aebfd798d86fb2bddc5986f4bf9579571a82843d1c7a79f3bb with
x1,
x3,
x5,
x7,
x8,
x9,
λ x11 x12 . 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_5fb65c286094f09917b7164094190b9100eedf8a4a5a58046fe9cc19dbc4a496 with
x0,
x2,
x4,
x6,
x8,
x9,
λ x10 x11 . 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 . e3162.. (f482f.. x11 (4ae4a.. (4ae4a.. 4a7ef..))) x8 x9 = x5 x8 x9.
Let x10 of type ι → ι → ο be given.
Apply unknownprop_5fb65c286094f09917b7164094190b9100eedf8a4a5a58046fe9cc19dbc4a496 with
x1,
x3,
x5,
x7,
x8,
x9,
λ x11 x12 . x10 x12 x11 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L6.
Apply unknownprop_49a26ed2e8c0e85eaecde06670270561b837d7f07fac28648201cb284750f907 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_49a26ed2e8c0e85eaecde06670270561b837d7f07fac28648201cb284750f907 with x1, x3, x5, x7, λ x9 x10 . x8 x10 x9.