Let x0 of type ι be given.

Assume H0: Field x0.

Apply H0 with ∀ x1 . x1 ∈ K_field_0 x0 x0 ⟶ ∀ x2 . x2 ∈ K_field_0 x0 x0 ⟶ K_field_1_b x0 x0 x1 x2 ∈ K_field_0 x0 x0.

Apply unknownprop_e08b2452b1a2fc464ffe03692b94bd4650b3a041709d65cf5d5d9c41083a3cb8 with x0, λ x1 x2 . struct_b_b_e_e x2 ⟶ unpack_b_b_e_e_o x0 (λ x3 . λ x4 x5 : ι → ι → ι . λ x6 x7 . explicit_Field x3 x6 x7 x4 x5) ⟶ ∀ x3 . x3 ∈ K_field_0 x0 x0 ⟶ ∀ x4 . x4 ∈ K_field_0 x0 x0 ⟶ K_field_1_b x0 x0 x3 x4 ∈ K_field_0 x0 x0 leaving 2 subgoals.

The subproof is completed by applying H0.

Assume H1: struct_b_b_e_e (pack_b_b_e_e (K_field_0 x0 x0) (K_field_1_b x0 x0) (K_field_2_b x0 x0) (K_field_3 x0 x0) (K_field_4 x0 x0)).

Assume H2: unpack_b_b_e_e_o x0 (λ x1 . λ x2 x3 : ι → ι → ι . λ x4 x5 . explicit_Field x1 x4 x5 x2 x3).

Apply pack_struct_b_b_e_e_E1 with K_field_0 x0 x0, K_field_1_b x0 x0, K_field_2_b x0 x0, K_field_3 x0 x0, K_field_4 x0 x0.

The subproof is completed by applying H1.

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Proofgold Proof