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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.
Let x2 of type ι be given.
Assume H2: x2 ∈ field0 x0.
Let x3 of type ι be given.
Assume H3: x3 ∈ field0 x0.
Assume H4: RealsStruct_lt x0 x1 x2.
Assume H5: RealsStruct_lt x0 x2 x3.
Apply H4 with RealsStruct_lt x0 x1 x3.
Assume H6: RealsStruct_leq x0 x1 x2.
Assume H7: x1 = x2 ⟶ ∀ x4 : ο . x4.
Apply RealsStruct_leq_lt_tra with x0, x1, x2, x3 leaving 6 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.
The subproof is completed by applying H6.
The subproof is completed by applying H5.
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