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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: RealsStruct x0.
Let x1 of type ι be given.
Assume H1: x1 ∈ field0 x0.
Assume H2: RealsStruct_lt x0 x1 (field4 x0).
Claim L3: not (RealsStruct_leq x0 (field4 x0) x1)
Assume H3: RealsStruct_leq x0 (field4 x0) x1.
Apply RealsStruct_lt_leq_asym with x0, x1, field4 x0 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply RealsStruct_zero_In with x0.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Apply If_i_0 with RealsStruct_leq x0 (field4 x0) x1, x1, Field_minus (Field_of_RealsStruct x0) x1.
The subproof is completed by applying L3.
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