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.
Assume H1: x0 ⊆ x1.
Apply GroupE with
x1,
x3.
The subproof is completed by applying H0.
Let x4 of type ι → ι → ι be given.
Assume H3: ∀ x5 . x5 ∈ x1 ⟶ ∀ x6 . x6 ∈ x1 ⟶ x3 x5 x6 = x4 x5 x6.
Apply unknownprop_6f443acda8c525028830077e56d25cc42421b356ff555ec80c66f7077fb21a6f with
x0,
x1,
x2,
x3,
λ x5 x6 : ο . unpack_b_o (pack_b x0 x2) (λ x7 . λ x8 : ι → ι → ι . explicit_normal x1 x4 x7) = x6.
Apply unknownprop_6f443acda8c525028830077e56d25cc42421b356ff555ec80c66f7077fb21a6f with
x0,
x1,
x2,
x4,
λ x5 x6 : ο . x6 = explicit_normal x1 x3 x0.
Let x5 of type ο → ο → ο be given.
Apply unknownprop_7cb03a255d2fec9c7695b2dda3bc3dd2780cc664df29cae9822c5b34ef1bd688 with
x0,
x1,
x3,
x4,
λ x6 x7 : ο . x5 x7 x6 leaving 3 subgoals.
The subproof is completed by applying L2.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
Apply unpack_b_o_eq with
λ x4 . λ x5 : ι → ι → ι . unpack_b_o (pack_b x0 x2) (λ x6 . λ x7 : ι → ι → ι . explicit_normal x4 x5 x6),
x1,
x3,
λ x4 x5 : ο . x5 = explicit_normal x1 x3 x0 leaving 2 subgoals.
The subproof is completed by applying L3.
The subproof is completed by applying unknownprop_6f443acda8c525028830077e56d25cc42421b356ff555ec80c66f7077fb21a6f with x0, x1, x2, x3.