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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.
Apply RealsStruct_lt_trich_impred with x0, x1, x2, or (or (RealsStruct_lt x0 x1 x2) (x1 = x2)) (RealsStruct_lt x0 x2 x1) leaving 6 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Assume H3: RealsStruct_lt x0 x1 x2.
Apply orIL with or (RealsStruct_lt x0 x1 x2) (x1 = x2), RealsStruct_lt x0 x2 x1.
Apply orIL with RealsStruct_lt x0 x1 x2, x1 = x2.
The subproof is completed by applying H3.
Assume H3: x1 = x2.
Apply orIL with or (RealsStruct_lt x0 x1 x2) (x1 = x2), RealsStruct_lt x0 x2 x1.
Apply orIR with RealsStruct_lt x0 x1 x2, x1 = x2.
The subproof is completed by applying H3.
Assume H3: RealsStruct_lt x0 x2 x1.
Apply orIR with or (RealsStruct_lt x0 x1 x2) (x1 = x2), RealsStruct_lt x0 x2 x1.
The subproof is completed by applying H3.
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