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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι → ι → ι be given.
Assume H0: explicit_Group x0 x1.
Let x2 of type ι be given.
Assume H1: x2 ∈ x0.
Apply explicit_Group_inverse_prop with x0, x1, x2, explicit_Group_inverse x0 x1 x2 ∈ x0 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Assume H2: explicit_Group_inverse x0 x1 x2 ∈ x0.
Assume H3: and (x1 x2 (explicit_Group_inverse x0 x1 x2) = explicit_Group_identity x0 x1) (x1 (explicit_Group_inverse x0 x1 x2) x2 = explicit_Group_identity x0 x1).
The subproof is completed by applying H2.
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