Proofgold Proof

pf

Let x0 of type ι be given.

Assume H0: Field x0.

Apply H0 with explicit_Field (K_field_0 x0 x0) (K_field_3 x0 x0) (K_field_4 x0 x0) (K_field_1_b x0 x0) (K_field_2_b x0 x0).

Assume H1: struct_b_b_e_e x0.

Apply unknownprop_e08b2452b1a2fc464ffe03692b94bd4650b3a041709d65cf5d5d9c41083a3cb8 with x0, λ x1 x2 . unpack_b_b_e_e_o x2 (λ x3 . λ x4 x5 : ι → ι → ι . λ x6 x7 . explicit_Field x3 x6 x7 x4 x5) ⟶ explicit_Field (K_field_0 x0 x0) (K_field_3 x0 x0) (K_field_4 x0 x0) (K_field_1_b x0 x0) (K_field_2_b x0 x0) leaving 2 subgoals.

The subproof is completed by applying H0.

Apply Field_unpack_eq 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, λ x1 x2 : ο . x2 ⟶ explicit_Field (K_field_0 x0 x0) (K_field_3 x0 x0) (K_field_4 x0 x0) (K_field_1_b x0 x0) (K_field_2_b x0 x0).

Assume H2: explicit_Field (K_field_0 x0 x0) (K_field_3 x0 x0) (K_field_4 x0 x0) (K_field_1_b x0 x0) (K_field_2_b x0 x0).

The subproof is completed by applying H2.

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