Let x0 of type ι be given.
Apply RealsStruct_plus_cancelL with
x0,
field4 x0,
Field_minus (Field_of_RealsStruct x0) (field4 x0),
field4 x0 leaving 5 subgoals.
The subproof is completed by applying H0.
Apply RealsStruct_zero_In with
x0.
The subproof is completed by applying H0.
Apply RealsStruct_minus_clos with
x0,
field4 x0 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply RealsStruct_zero_In with
x0.
The subproof is completed by applying H0.
Apply RealsStruct_zero_In with
x0.
The subproof is completed by applying H0.
Apply RealsStruct_zero_L with
x0,
field4 x0,
λ x1 x2 . field1b x0 (field4 x0) (Field_minus (Field_of_RealsStruct x0) (field4 x0)) = x2 leaving 3 subgoals.
The subproof is completed by applying H0.
Apply RealsStruct_zero_In with
x0.
The subproof is completed by applying H0.
Apply RealsStruct_minus_R with
x0,
field4 x0 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply RealsStruct_zero_In with
x0.
The subproof is completed by applying H0.