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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ιιι be given.
Let x2 of type ι be given.
Assume H0: 4f2b4.. (987b2.. x0 x1).
Assume H1: 7fe8f.. x0 x1 x2.
Claim L2: explicit_Group x0 x1
Apply unknownprop_92c6fa644c6dced27956132c489750908a0c8c60a2c0fd4eb67751c9bc54bfc0 with x0, x1.
The subproof is completed by applying H0.
Claim L3: explicit_Group x2 x1
Apply H1 with explicit_Group x2 x1.
Assume H3: 4f2b4.. (987b2.. x2 x1).
Assume H4: Subq x2 x0.
Apply unknownprop_92c6fa644c6dced27956132c489750908a0c8c60a2c0fd4eb67751c9bc54bfc0 with x2, x1.
The subproof is completed by applying H3.
Claim L4: Subq x2 x0
Apply H1 with Subq x2 x0.
Assume H4: 4f2b4.. (987b2.. x2 x1).
Assume H5: Subq x2 x0.
The subproof is completed by applying H5.
Let x3 of type ι be given.
Assume H5: prim1 x3 x2.
Claim L6: prim1 x3 x0
Apply L4 with x3.
The subproof is completed by applying H5.
Claim L7: prim1 (explicit_Group_inverse x2 x1 x3) x0
Apply L4 with explicit_Group_inverse x2 x1 x3.
Apply explicit_Group_inverse_in with x2, x1, x3 leaving 2 subgoals.
The subproof is completed by applying L3.
The subproof is completed by applying H5.
Claim L8: prim1 (explicit_Group_inverse x0 x1 x3) x0
Apply explicit_Group_inverse_in with x0, x1, x3 leaving 2 subgoals.
The subproof is completed by applying L2.
The subproof is completed by applying L6.
Apply explicit_Group_lcancel with x0, x1, x3, explicit_Group_inverse x0 x1 x3, explicit_Group_inverse x2 x1 x3 leaving 5 subgoals.
The subproof is completed by applying L2.
The subproof is completed by applying L6.
The subproof is completed by applying L8.
The subproof is completed by applying L7.
Apply explicit_Group_inverse_rinv with x0, x1, x3, λ x4 x5 . x5 = x1 x3 (explicit_Group_inverse x2 x1 x3) leaving 3 subgoals.
The subproof is completed by applying L2.
The subproof is completed by applying L6.
Apply explicit_Group_inverse_rinv with x2, x1, x3, λ x4 x5 . explicit_Group_identity x0 x1 = x5 leaving 3 subgoals.
The subproof is completed by applying L3.
The subproof is completed by applying H5.
Apply unknownprop_3b6332b574f8798946aa227382184940cc8835dc642594c2dfe0ae12578e0c83 with x0, x1, x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.