Proofgold Proof

pf

Let x0 of type ι be given.

Assume H0: CRing_with_id x0.

Apply H0 with field3 x0 ∈ 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) ⟶ field3 x0 ∈ field0 x0 leaving 2 subgoals.

The subproof is completed by applying H0.

Assume H1: struct_b_b_e_e (pack_b_b_e_e (field0 x0) (field1b x0) (field2b x0) (field3 x0) (field4 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 field0 x0, field1b x0, field2b x0, field3 x0, field4 x0.

The subproof is completed by applying H1.

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