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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: SNo x0.
Assume H1: SNo x1.
Assume H2: SNo x2.
Apply unknownprop_a0f3a6ba21e0d8abfdec3b7e6006847345d02f100b1717119011962dd7d33428 with x0, x1, SNoLe x1 x2SNoLe x0 x2.
Assume H3: PNoLe (SNoLev x0) (λ x3 . In x3 x0) (SNoLev x1) (λ x3 . In x3 x1).
Apply unknownprop_a0f3a6ba21e0d8abfdec3b7e6006847345d02f100b1717119011962dd7d33428 with x1, x2, SNoLe x0 x2.
Assume H4: PNoLe (SNoLev x1) (λ x3 . In x3 x1) (SNoLev x2) (λ x3 . In x3 x2).
Apply unknownprop_7f3377c88b4409d85225bd10726cc6caca85db3671a8e3d8d0e75f9aea9723e4 with x0, x2.
Apply unknownprop_e94a13b4ac63cce4a867fc33d11c1ef6b397fe3905a6599da4996709c5166382 with SNoLev x0, SNoLev x1, SNoLev x2, λ x3 . In x3 x0, λ x3 . In x3 x1, λ x3 . In x3 x2 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.
Apply unknownprop_1a147113790e251cd62150dc8f2ccc18199f0d805bd5862263191a1a0d2a0c36 with x2.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.