Let x0 of type ι be given.

Apply H0 with ∀ x1 . x1 ∈ field0 x0 ⟶ ∀ x2 . x2 ∈ field0 x0 ⟶ field1b x0 x1 x2 ∈ field0 x0.

Apply CRing_with_id_eta 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) ⟶ ∀ x3 . x3 ∈ field0 x0 ⟶ ∀ x4 . x4 ∈ field0 x0 ⟶ field1b x0 x3 x4 ∈ field0 x0 leaving 2 subgoals.

The subproof is completed by applying H0.

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_E1 with field0 x0, field1b x0, field2b x0, field3 x0, field4 x0.

The subproof is completed by applying H1.

■

Proofgold Proof