Let x0 of type ι be given.
Apply Field_minus_eq with
x0,
field3 x0,
λ x1 x2 . x2 = field3 x0 leaving 3 subgoals.
The subproof is completed by applying H0.
Apply Field_zero_In with
x0.
The subproof is completed by applying H0.
Apply explicit_Field_minus_zero with
field0 x0,
field3 x0,
field4 x0,
field1b x0,
field2b x0.
Apply Field_explicit_Field with
x0.
The subproof is completed by applying H0.