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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Assume H0: prim1 x2 (0ac37.. x0 x1).
Apply UnionE_impred with prim2 x0 x1, x2, or (prim1 x2 x0) (prim1 x2 x1) leaving 2 subgoals.
The subproof is completed by applying H0.
Let x3 of type ι be given.
Assume H1: prim1 x2 x3.
Assume H2: prim1 x3 (prim2 x0 x1).
Apply unknownprop_44132e34b8fcc92e54ff875d0e8f6137eeea7d41bb9d4b117dbbbb4d2f239782 with x3, x0, x1, or (prim1 x2 x0) (prim1 x2 x1) leaving 3 subgoals.
The subproof is completed by applying H2.
Assume H3: x3 = x0.
Apply orIL with prim1 x2 x0, prim1 x2 x1.
Apply H3 with λ x4 x5 . prim1 x2 x4.
The subproof is completed by applying H1.
Assume H3: x3 = x1.
Apply orIR with prim1 x2 x0, prim1 x2 x1.
Apply H3 with λ x4 x5 . prim1 x2 x4.
The subproof is completed by applying H1.