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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 → ο be given.
Let x7 of type ι → ο be given.
Let x8 of type ι → ο be given.
Let x9 of type ι → ο be given.
Claim L2: x0 = x1
Apply L1 with λ x10 x11 . x0 = x11.
Apply and5I with x0 = x1, ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ x2 x10 x11 = x3 x10 x11, ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ x4 x10 x11 = x5 x10 x11, ∀ x10 . x10 ∈ x0 ⟶ x6 x10 = x7 x10, ∀ x10 . x10 ∈ x0 ⟶ x8 x10 = x9 x10 leaving 5 subgoals.
The subproof is completed by applying L2.
Let x10 of type ι be given.
Assume H3: x10 ∈ x0.
Let x11 of type ι be given.
Assume H4: x11 ∈ x0.
Apply pack_r_r_p_p_1_eq2 with x0, x2, x4, x6, x8, x10, x11, λ x12 x13 : ο . x13 = x3 x10 x11 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Claim L5: x10 ∈ x1
Apply L2 with λ x12 x13 . x10 ∈ x12.
The subproof is completed by applying H3.
Claim L6: x11 ∈ x1
Apply L2 with λ x12 x13 . x11 ∈ x12.
The subproof is completed by applying H4.
Apply H0 with λ x12 x13 . decode_r (ap x13 1) x10 x11 = x3 x10 x11.
Let x12 of type ο → ο → ο be given.
Apply pack_r_r_p_p_1_eq2 with x1, x3, x5, x7, x9, x10, x11, λ x13 x14 : ο . x12 x14 x13 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L6.
Let x10 of type ι be given.
Assume H3: x10 ∈ x0.
Let x11 of type ι be given.
Assume H4: x11 ∈ x0.
Apply pack_r_r_p_p_2_eq2 with x0, x2, x4, x6, x8, x10, x11, λ x12 x13 : ο . x13 = x5 x10 x11 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Claim L5: x10 ∈ x1
Apply L2 with λ x12 x13 . x10 ∈ x12.
The subproof is completed by applying H3.
Claim L6: x11 ∈ x1
Apply L2 with λ x12 x13 . x11 ∈ x12.
The subproof is completed by applying H4.
Apply H0 with λ x12 x13 . decode_r (ap x13 2) x10 x11 = x5 x10 x11.
Let x12 of type ο → ο → ο be given.
Apply pack_r_r_p_p_2_eq2 with x1, x3, x5, x7, x9, x10, x11, λ x13 x14 : ο . x12 x14 x13 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L6.
Let x10 of type ι be given.
Assume H3: x10 ∈ x0.
Apply pack_r_r_p_p_3_eq2 with x0, x2, x4, x6, x8, x10, λ x11 x12 : ο . x12 = x7 x10 leaving 2 subgoals.
The subproof is completed by applying H3.
Claim L4: x10 ∈ x1
Apply L2 with λ x11 x12 . x10 ∈ x11.
The subproof is completed by applying H3.
Apply H0 with λ x11 x12 . decode_p (ap x12 3) x10 = x7 x10.
Let x11 of type ο → ο → ο be given.
Apply pack_r_r_p_p_3_eq2 with x1, x3, x5, x7, x9, x10, λ x12 x13 : ο . x11 x13 x12.
The subproof is completed by applying L4.
Let x10 of type ι be given.
Assume H3: x10 ∈ x0.
Apply pack_r_r_p_p_4_eq2 with x0, x2, x4, x6, x8, x10, λ x11 x12 : ο . x12 = x9 x10 leaving 2 subgoals.
The subproof is completed by applying H3.
Claim L4: x10 ∈ x1
Apply L2 with λ x11 x12 . x10 ∈ x11.
The subproof is completed by applying H3.
Apply H0 with λ x11 x12 . decode_p (ap x12 4) x10 = x9 x10.
Let x11 of type ο → ο → ο be given.
Apply pack_r_r_p_p_4_eq2 with x1, x3, x5, x7, x9, x10, λ x12 x13 : ο . x11 x13 x12.
The subproof is completed by applying L4.
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