Let x0 of type ι be given.
Let x1 of type ι be given.
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.