Let x0 of type ι be given.

Apply H0 with K_field_3 x0 x0 ∈ K_field_0 x0 x0.

Apply unknownprop_50ae0d1c45204b46a4fcc7a6bee445594122c11b111b42c080baae0465265b26 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_CRing_with_id x3 x6 x7 x4 x5) ⟶ K_field_3 x0 x0 ∈ 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_CRing_with_id x1 x4 x5 x2 x3).

Apply pack_struct_b_b_e_e_E3 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.

■

Proofgold Proof