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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: Field x0.
Let x1 of type ι be given.
Assume H1: x1field0 x0.
Apply Field_minus_eq with x0, x1, λ x2 x3 . field1b x0 x1 x3 = field3 x0 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply explicit_Field_minus_R with field0 x0, field3 x0, field4 x0, field1b x0, field2b x0, x1 leaving 2 subgoals.
Apply Field_explicit_Field with x0.
The subproof is completed by applying H0.
The subproof is completed by applying H1.