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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, SNoLe x1 x0 ⟶ x0 = x1.
Assume H2: PNoLe (SNoLev x0) (λ x2 . In x2 x0) (SNoLev x1) (λ x2 . In x2 x1).
Apply unknownprop_a0f3a6ba21e0d8abfdec3b7e6006847345d02f100b1717119011962dd7d33428 with x1, x0, x0 = x1.
Assume H3: PNoLe (SNoLev x1) (λ x2 . In x2 x1) (SNoLev x0) (λ x2 . In x2 x0).
Apply unknownprop_cfdf4f94c8dcd8d32ef4ff3bb2d978e062c9ed9bc8ff3a2ee8cc127f8f333bd3 with SNoLev x0, SNoLev x1, λ x2 . In x2 x0, λ x2 . In x2 x1, x0 = x1 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.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Assume H4: SNoLev x0 = SNoLev x1.
Assume H5: PNoEq_ (SNoLev x0) (λ x2 . In x2 x0) (λ x2 . In x2 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 H4.
Apply unknownprop_e65d4a6131bd0f3fcd91fa1f20b9cfd36b0cf97f8c821750cc7f8f971a40e6bb with SNoLev x0, x0, x1.
The subproof is completed by applying H5.
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