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: prim1 x2 x0.

Apply explicit_Group_inverse_prop with x0, x1, x2, x1 x2 (explicit_Group_inverse x0 x1 x2) = explicit_Group_identity x0 x1 leaving 3 subgoals.

The subproof is completed by applying H0.

The subproof is completed by applying H1.

Assume H2: prim1 (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).

Apply H3 with x1 x2 (explicit_Group_inverse x0 x1 x2) = explicit_Group_identity x0 x1.

Assume H4: x1 x2 (explicit_Group_inverse x0 x1 x2) = explicit_Group_identity x0 x1.

Assume H5: x1 (explicit_Group_inverse x0 x1 x2) x2 = explicit_Group_identity x0 x1.

The subproof is completed by applying H4.

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