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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: SNo x0.
Assume H1: SNo x1.
Apply unknownprop_b79cb1702e8ed87da3fa15a463d1286cd0e769d607a361b393d7ac2b561606df with SNoLev x0, SNoLev x1, λ x2 . In x2 x0, λ x2 . In x2 x1, or (or (SNoLt x0 x1) (x0 = x1)) (SNoLt x1 x0) leaving 5 subgoals.
Apply unknownprop_1a147113790e251cd62150dc8f2ccc18199f0d805bd5862263191a1a0d2a0c36 with x0.
The subproof is completed by applying H0.
Apply unknownprop_1a147113790e251cd62150dc8f2ccc18199f0d805bd5862263191a1a0d2a0c36 with x1.
The subproof is completed by applying H1.
Assume H2: PNoLt (SNoLev x0) (λ x2 . In x2 x0) (SNoLev x1) (λ x2 . In x2 x1).
Apply unknownprop_0e1ba7291a295ea3c1979b40483f7544221790d53d76aadba99638689b88d9d1 with SNoLt x0 x1, x0 = x1, SNoLt x1 x0.
Apply unknownprop_7cfd5e4aadf2e8cb5956c30c3589cd3b6084bd1797b4cd3169e2a989d66e37fe with x0, x1.
The subproof is completed by applying H2.
Assume H2: SNoLev x0 = SNoLev x1.
Assume H3: PNoEq_ (SNoLev x0) (λ x2 . In x2 x0) (λ x2 . In x2 x1).
Apply unknownprop_55d33d10f6a09aaaea8e002117cf1820d9dc4418a57f04c18d4ec79694021a99 with SNoLt x0 x1, x0 = x1, SNoLt x1 x0.
Apply unknownprop_74792b8cbb4aec2c214f839cffc7a63ac0ac44cf37a6c1a18253d9ac8ad5be9e 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 H2.
Apply unknownprop_e65d4a6131bd0f3fcd91fa1f20b9cfd36b0cf97f8c821750cc7f8f971a40e6bb with SNoLev x0, x0, x1.
The subproof is completed by applying H3.
Assume H2: PNoLt (SNoLev x1) (λ x2 . In x2 x1) (SNoLev x0) (λ x2 . In x2 x0).
Apply unknownprop_c33a8518d3fc8314286e0e0f7acdb4e408d0225cb1257a73db3a51552718bbdd with SNoLt x0 x1, x0 = x1, SNoLt x1 x0.
Apply unknownprop_7cfd5e4aadf2e8cb5956c30c3589cd3b6084bd1797b4cd3169e2a989d66e37fe with x1, x0.
The subproof is completed by applying H2.
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