Let x0 of type ι be given.
Let x1 of type ι be given.
Apply RealsStruct_minus_clos with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply explicit_Field_minus_clos with
field0 x0,
field4 x0,
RealsStruct_one x0,
field1b x0,
field2b x0,
x1 leaving 2 subgoals.
Apply explicit_Field_of_RealsStruct with
x0.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply RealsStruct_plus_cancelL with
x0,
x1,
Field_minus (Field_of_RealsStruct x0) x1,
explicit_Field_minus (field0 x0) (field4 x0) (RealsStruct_one x0) (field1b x0) (field2b x0) x1 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying L2.
The subproof is completed by applying L3.
Apply RealsStruct_minus_R with
x0,
x1,
λ x2 x3 . x3 = field1b x0 x1 (explicit_Field_minus (field0 x0) (field4 x0) (RealsStruct_one x0) (field1b x0) (field2b x0) x1) leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Let x2 of type ι → ι → ο be given.
Apply explicit_Field_minus_R with
field0 x0,
field4 x0,
RealsStruct_one x0,
field1b x0,
field2b x0,
x1,
λ x3 x4 . x2 x4 x3 leaving 2 subgoals.
Apply explicit_Field_of_RealsStruct with
x0.
The subproof is completed by applying H0.
The subproof is completed by applying H1.