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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_a0f3a6ba21e0d8abfdec3b7e6006847345d02f100b1717119011962dd7d33428 with x0, x1, or (SNoLt x0 x1) (x0 = x1).
Assume H2: PNoLe (SNoLev x0) (λ x2 . In x2 x0) (SNoLev x1) (λ x2 . In x2 x1).
Apply unknownprop_a0b9870a33f18f7eb5aaf7ae107d529d6499166437a3535589b34653050e816a with SNoLev x0, SNoLev x1, λ x2 . In x2 x0, λ x2 . In x2 x1, or (SNoLt x0 x1) (x0 = x1) leaving 3 subgoals.
The subproof is completed by applying H2.
Assume H3: PNoLt (SNoLev x0) (λ x2 . In x2 x0) (SNoLev x1) (λ x2 . In x2 x1).
Apply unknownprop_7c688f24c3595bc4b513e911d7f551c8ccfedc804a6c15c02d25d01a2996aec6 with SNoLt x0 x1, x0 = x1.
Apply unknownprop_7cfd5e4aadf2e8cb5956c30c3589cd3b6084bd1797b4cd3169e2a989d66e37fe with x0, x1.
The subproof is completed by applying H3.
Assume H3: SNoLev x0 = SNoLev x1.
Assume H4: PNoEq_ (SNoLev x0) (λ x2 . In x2 x0) (λ x2 . In x2 x1).
Apply unknownprop_c29620ea10188dd8ed7659bc2875dc8e08f16ffd29713f8ee3146f02f9828ceb with SNoLt x0 x1, x0 = x1.
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 H3.
Apply unknownprop_e65d4a6131bd0f3fcd91fa1f20b9cfd36b0cf97f8c821750cc7f8f971a40e6bb with SNoLev x0, x0, x1.
The subproof is completed by applying H4.
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