Let x0 of type ι → ο be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Assume H1: x0 x1.
Assume H2: x0 x2.
Apply H0 with
x1,
λ x4 . Hom_b_b_e_e x4 x2 x3 ⟶ x3 ∈ setexp (ap x2 0) (ap x4 0) leaving 2 subgoals.
The subproof is completed by applying H1.
Let x4 of type ι be given.
Let x5 of type ι → ι → ι be given.
Assume H3: ∀ x6 . x6 ∈ x4 ⟶ ∀ x7 . x7 ∈ x4 ⟶ x5 x6 x7 ∈ x4.
Let x6 of type ι → ι → ι be given.
Assume H4: ∀ x7 . x7 ∈ x4 ⟶ ∀ x8 . x8 ∈ x4 ⟶ x6 x7 x8 ∈ x4.
Let x7 of type ι be given.
Assume H5: x7 ∈ x4.
Let x8 of type ι be given.
Assume H6: x8 ∈ x4.
Apply H0 with
x2,
λ x9 . Hom_b_b_e_e (pack_b_b_e_e x4 x5 x6 x7 x8) x9 x3 ⟶ x3 ∈ setexp (ap x9 0) (ap (pack_b_b_e_e x4 x5 x6 x7 x8) 0) leaving 2 subgoals.
The subproof is completed by applying H2.
Let x9 of type ι be given.
Let x10 of type ι → ι → ι be given.
Assume H7: ∀ x11 . x11 ∈ x9 ⟶ ∀ x12 . x12 ∈ x9 ⟶ x10 x11 x12 ∈ x9.
Let x11 of type ι → ι → ι be given.
Assume H8: ∀ x12 . x12 ∈ x9 ⟶ ∀ x13 . x13 ∈ x9 ⟶ x11 x12 x13 ∈ x9.
Let x12 of type ι be given.
Assume H9: x12 ∈ x9.
Let x13 of type ι be given.
Assume H10: x13 ∈ x9.
Apply unknownprop_c390c3300969ceff9fa6146a517f8bd0892446bb27336e3269cdaa03d494c7b4 with
x4,
x9,
x5,
x6,
x10,
x11,
x7,
x8,
x12,
x13,
x3,
λ x14 x15 : ο . x15 ⟶ x3 ∈ setexp (ap (pack_b_b_e_e x9 x10 x11 x12 x13) 0) (ap (pack_b_b_e_e x4 x5 x6 x7 x8) 0).
Assume H11:
and (and (and (and (x3 ∈ setexp x9 x4) (∀ x14 . x14 ∈ x4 ⟶ ∀ x15 . x15 ∈ x4 ⟶ ap x3 (x5 x14 x15) = x10 (ap x3 x14) (ap x3 x15))) (∀ x14 . x14 ∈ x4 ⟶ ∀ x15 . x15 ∈ x4 ⟶ ap x3 (x6 x14 x15) = x11 (ap x3 x14) (ap x3 x15))) (ap x3 x7 = x12)) (ap x3 x8 = x13).
Apply pack_b_b_e_e_0_eq2 with
x9,
x10,
x11,
x12,
x13,
λ x14 x15 . x3 ∈ setexp x14 (ap (pack_b_b_e_e x4 x5 x6 x7 x8) 0).
Apply pack_b_b_e_e_0_eq2 with
x4,
x5,
x6,
x7,
x8,
λ x14 x15 . x3 ∈ setexp x9 x14.
Apply H11 with
x3 ∈ setexp x9 ....
Apply unknownprop_cb7abf829499aec888363ff9292dd7680786c42dc92f10fdd88dc16ada048723 with
x0,
λ x1 . ap x1 0,
Hom_b_b_e_e.
The subproof is completed by applying L1.