Let x0 of type ι be given.
Let x1 of type ι be given.
Apply RealsStruct_leq_lt_linear with
x0,
field4 x0,
x1,
RealsStruct_abs x0 x1 = field4 x0 ⟶ x1 = 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.
The subproof is completed by applying H1.
Apply RealsStruct_abs_nonneg_case with
x0,
x1,
λ x2 x3 . x3 = field4 x0 ⟶ x1 = field4 x0 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Apply RealsStruct_abs_neg_case with
x0,
x1,
λ x2 x3 . x3 = field4 x0 ⟶ x1 = field4 x0 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply RealsStruct_minus_invol with
x0,
x1,
λ x2 x3 . x2 = field4 x0 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.