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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: ordinal x0.
Apply unknownprop_b257b354d80b58d9a8444b167a21f47b4aabc910dc3698404491d5ef01e18cf3 with ∃ x1 . and (In x1 x0) (x0 = ordsucc x1), or (∀ x1 . In x1 x0 ⟶ In (ordsucc x1) x0) (∃ x1 . and (In x1 x0) (x0 = ordsucc x1)) leaving 2 subgoals.
Assume H1: ∃ x1 . and (In x1 x0) (x0 = ordsucc x1).
Apply unknownprop_c29620ea10188dd8ed7659bc2875dc8e08f16ffd29713f8ee3146f02f9828ceb with ∀ x1 . In x1 x0 ⟶ In (ordsucc x1) x0, ∃ x1 . and (In x1 x0) (x0 = ordsucc x1).
The subproof is completed by applying H1.
Assume H1: not (∃ x1 . and (In x1 x0) (x0 = ordsucc x1)).
Apply unknownprop_7c688f24c3595bc4b513e911d7f551c8ccfedc804a6c15c02d25d01a2996aec6 with ∀ x1 . In x1 x0 ⟶ In (ordsucc x1) x0, ∃ x1 . and (In x1 x0) (x0 = ordsucc x1).
Let x1 of type ι be given.
Assume H2: In x1 x0.
Apply unknownprop_eb8e8f72a91f1b934993d4cb19c84c8270f73a3626f3022b683d960a7fef89cb with In (ordsucc x1) x0, x0 = ordsucc x1, In (ordsucc x1) x0 leaving 3 subgoals.
Apply unknownprop_2539815e221739e5ed231d021c9e8622ca0ca73d6737f4a44b47896fd145c3c2 with x0, x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
Assume H3: In (ordsucc x1) x0.
The subproof is completed by applying H3.
Assume H3: x0 = ordsucc x1.
Apply FalseE with In (ordsucc x1) x0.
Apply notE with ∃ x2 . and (In x2 x0) (x0 = ordsucc x2) leaving 2 subgoals.
The subproof is completed by applying H1.
Let x2 of type ο be given.
Assume H4: ∀ x3 . and (In x3 x0) (x0 = ordsucc x3) ⟶ x2.
Apply H4 with x1.
Apply unknownprop_389e2fb1855352fcc964ea44fe6723d7a1c2d512f04685300e3e97621725b977 with In x1 x0, x0 = ordsucc x1 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
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