Let x0 of type ι be given.
Let x1 of type ι be given.
Apply RealsStruct_plus_com with
x0,
Field_minus (Field_of_RealsStruct x0) x1,
x1,
λ x2 x3 . x3 = field4 x0 leaving 4 subgoals.
The subproof is completed by applying H0.
Apply RealsStruct_minus_clos with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H1.
Apply RealsStruct_minus_R with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.