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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 → ι → ο be given.
Let x7 of type ι → ι → ο be given.
Let x8 of type ι be given.
Let x9 of type ι be given.
Let x10 of type ι be given.
Let x11 of type ι be given.
Apply and6I with x0 = x1, ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ x2 x12 x13 = x3 x12 x13, ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ x4 x12 x13 = x5 x12 x13, ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ x6 x12 x13 = x7 x12 x13, x8 = x9, x10 = x11 leaving 6 subgoals.
The subproof is completed by applying L2.
Let x12 of type ι be given.
Assume H3: x12 ∈ x0.
Let x13 of type ι be given.
Assume H4: x13 ∈ x0.
Apply pack_b_b_r_e_e_1_eq2 with x0, x2, x4, x6, x8, x10, x12, x13, λ x14 x15 . x15 = x3 x12 x13 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Claim L5: x12 ∈ x1
Apply L2 with λ x14 x15 . x12 ∈ x14.
The subproof is completed by applying H3.
Claim L6: x13 ∈ x1
Apply L2 with λ x14 x15 . x13 ∈ x14.
The subproof is completed by applying H4.
Apply H0 with λ x14 x15 . decode_b (ap x15 1) x12 x13 = x3 x12 x13.
Let x14 of type ι → ι → ο be given.
Apply pack_b_b_r_e_e_1_eq2 with x1, x3, x5, x7, x9, x11, x12, x13, λ x15 x16 . x14 x16 x15 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L6.
Let x12 of type ι be given.
Assume H3: x12 ∈ x0.
Let x13 of type ι be given.
Assume H4: x13 ∈ x0.
Apply pack_b_b_r_e_e_2_eq2 with x0, x2, x4, x6, x8, x10, x12, x13, λ x14 x15 . x15 = x5 x12 x13 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Claim L5: x12 ∈ x1
Apply L2 with λ x14 x15 . x12 ∈ x14.
The subproof is completed by applying H3.
Claim L6: x13 ∈ x1
Apply L2 with λ x14 x15 . x13 ∈ x14.
The subproof is completed by applying H4.
Apply H0 with λ x14 x15 . decode_b (ap x15 2) x12 x13 = x5 x12 x13.
Let x14 of type ι → ι → ο be given.
Apply pack_b_b_r_e_e_2_eq2 with x1, x3, x5, x7, x9, x11, x12, x13, λ x15 x16 . x14 x16 x15 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L6.
Let x12 of type ι be given.
Assume H3: x12 ∈ x0.
Let x13 of type ι be given.
Assume H4: x13 ∈ x0.
Apply pack_b_b_r_e_e_3_eq2 with x0, x2, x4, x6, x8, x10, x12, x13, λ x14 x15 : ο . x15 = x7 x12 x13 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Claim L5: x12 ∈ x1
Apply L2 with λ x14 x15 . x12 ∈ x14.
The subproof is completed by applying H3.
Claim L6: x13 ∈ x1
Apply L2 with λ x14 x15 . x13 ∈ x14.
The subproof is completed by applying H4.
Apply H0 with λ x14 x15 . decode_r (ap x15 3) x12 x13 = x7 x12 x13.
Let x14 of type ο → ο → ο be given.
Apply pack_b_b_r_e_e_3_eq2 with x1, x3, x5, x7, x9, x11, x12, x13, λ x15 x16 : ο . x14 x16 x15 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L6.
Apply pack_b_b_r_e_e_4_eq2 with x0, x2, x4, x6, x8, x10, λ x12 x13 . x13 = x9.
Apply H0 with λ x12 x13 . ap x13 4 = x9.
Let x12 of type ι → ι → ο be given.
The subproof is completed by applying pack_b_b_r_e_e_4_eq2 with x1, x3, x5, x7, x9, x11, λ x13 x14 . x12 x14 ....
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