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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: 80242.. x0.
Assume H1: 80242.. x1.
Assume H2: 35b9b.. (e4431.. x0) (λ x2 . prim1 x2 x0) (e4431.. x1) (λ x2 . prim1 x2 x1).
Apply H2 with or (099f3.. x0 x1) (x0 = x1) leaving 2 subgoals.
Assume H3: 40dde.. (e4431.. x0) (λ x2 . prim1 x2 x0) (e4431.. x1) (λ x2 . prim1 x2 x1).
Apply orIL with 099f3.. x0 x1, x0 = x1.
The subproof is completed by applying H3.
Assume H3: and (e4431.. x0 = e4431.. x1) (PNoEq_ (e4431.. x0) (λ x2 . prim1 x2 x0) (λ x2 . prim1 x2 x1)).
Apply H3 with or (099f3.. x0 x1) (x0 = x1).
Assume H4: e4431.. x0 = e4431.. x1.
Assume H5: PNoEq_ (e4431.. x0) (λ x2 . prim1 x2 x0) (λ x2 . prim1 x2 x1).
Apply orIR with 099f3.. x0 x1, x0 = x1.
Apply unknownprop_c3102c186c7aa1001a5c1b1b7ecab6b25bcd639e713104221ece8bf414726a69 with x0, x1 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
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