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 → ο be given.
Let x5 of type ι → ι → ο be given.
Let x6 of type ι → ο be given.
Let x7 of type ι → ο be given.
Apply unknownprop_2f767463355b2be78a52215b09da638110c8c92004e7a0591312d77436e71248 with
81367.. 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_b420ee51d5d19ad980a4810713a3ef2428660a173fc05982fad8090ea4d95bd4 with x0, x2, x4, x6.
Apply and4I with
x0 = x1,
∀ x8 . prim1 x8 x0 ⟶ x2 x8 = x3 x8,
∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x4 x8 x9 = x5 x8 x9,
∀ 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_8adc62668ab8010ee4cf20ab2423c96fa058b125068a120ed3f4ac00a4a48e1d 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_8adc62668ab8010ee4cf20ab2423c96fa058b125068a120ed3f4ac00a4a48e1d 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.
Let x9 of type ι be given.
Apply unknownprop_2e831d5836c0f35ebf271acc4aaeb289f7e5a8e725e8249195a6239140317c54 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_2e831d5836c0f35ebf271acc4aaeb289f7e5a8e725e8249195a6239140317c54 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.
Apply unknownprop_29ad1a240e68bbe865919b85594b1639c5129575d9e47f21dcb92a9681f803d2 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_29ad1a240e68bbe865919b85594b1639c5129575d9e47f21dcb92a9681f803d2 with
x1,
x3,
x5,
x7,
x8,
λ x10 x11 : ο . x9 x11 x10.
The subproof is completed by applying L4.