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 be given.
Let x5 of type ι → ι be given.
Let x6 of type ι be given.
Let x7 of type ι be given.
Apply unknownprop_42196b468f7ee6900ff7a0764cb638961ca3510c86fc5044edb344cbf3b0bbb0 with
48567.. 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_443af384f5a766563c87fe1d5f5df83d020f061721e547989a9faf36c7e3644e 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 ⟶ x4 x8 = x5 x8,
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_e872f769d2f751d5ba4c285643abe39ba33ed9f3bd7608e4c63b386dc1f5861a 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_e872f769d2f751d5ba4c285643abe39ba33ed9f3bd7608e4c63b386dc1f5861a 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.
Apply unknownprop_aa5c741718ec84d60101c87f4b6d2bcc1b84ecd0ab92ad5cbef8a4e52fd8c3ad 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_aa5c741718ec84d60101c87f4b6d2bcc1b84ecd0ab92ad5cbef8a4e52fd8c3ad with
x1,
x3,
x5,
x7,
x8,
λ x10 x11 . x9 x11 x10.
The subproof is completed by applying L4.
Apply unknownprop_b6909c5dff1fb43ebdc001458c5897fbb3ef3b47c78c20e1838eb8e968585acb 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_b6909c5dff1fb43ebdc001458c5897fbb3ef3b47c78c20e1838eb8e968585acb with x1, x3, x5, x7, λ x9 x10 . x8 x10 x9.