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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ιιι be given.
Let x3 of type ιιι be given.
Assume H0: explicit_Ring x0 x1 x2 x3.
Let x4 of type ι be given.
Assume H1: x4x0.
Apply explicit_Ring_minus_prop with x0, x1, x2, x3, x4, x2 x4 (explicit_Ring_minus x0 x1 x2 x3 x4) = x1 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Assume H2: explicit_Ring_minus x0 x1 x2 x3 x4x0.
Assume H3: x2 x4 (explicit_Ring_minus x0 x1 x2 x3 x4) = x1.
The subproof is completed by applying H3.