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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: ordinal x1.
Assume H1: ordinal x2.
Assume H2: 1beb9.. x1 x0.
Assume H3: 1beb9.. x2 x0.
Let x3 of type ι be given.
Assume H4: prim1 x3 x1.
Apply H2 with prim1 x3 x2.
Assume H5: Subq x0 (472ec.. x1).
Assume H6: ∀ x4 . prim1 x4 x1exactly1of2 (prim1 (15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x0) (prim1 x4 x0).
Apply H3 with prim1 x3 x2.
Assume H7: Subq x0 (472ec.. x2).
Assume H8: ∀ x4 . prim1 x4 x2exactly1of2 (prim1 (15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x0) (prim1 x4 x0).
Claim L9: ...
...
Apply exactly1of2_or with prim1 ((λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3) x0, prim1 x3 x0, prim1 x3 x2 leaving 3 subgoals.
Apply H6 with x3.
The subproof is completed by applying H4.
Assume H10: prim1 ((λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3) x0.
Claim L11: prim1 ((λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3) (0ac37.. x2 (94f9e.. x2 (λ x4 . (λ x5 . 15418.. x5 (91630.. (4ae4a.. 4a7ef..))) x4)))
Apply H7 with (λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3.
The subproof is completed by applying H10.
Claim L12: or (prim1 ((λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3) x2) (prim1 ((λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3) (94f9e.. x2 (λ x4 . (λ x5 . 15418.. x5 (91630.. (4ae4a.. 4a7ef..))) x4)))
Apply unknownprop_b46721c187c37140cbae22d356b00ba89f4126d81d8665e4be15b5a58c78d06f with x2, 94f9e.. x2 (λ x4 . (λ x5 . 15418.. x5 (91630.. (4ae4a.. 4a7ef..))) x4), (λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3.
The subproof is completed by applying L11.
Apply L12 with prim1 x3 x2 leaving 2 subgoals.
Assume H13: prim1 ((λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3) x2.
Apply FalseE with prim1 x3 x2.
Apply unknownprop_d50cf015ad4bd21633c5a2d035ded36b98ffbab6f00fb800e392ce4bcc7ee247 with x2, x3 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H13.
Assume H13: prim1 ((λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3) (94f9e.. x2 (λ x4 . (λ x5 . 15418.. x5 (91630.. (4ae4a.. 4a7ef..))) x4)).
Apply unknownprop_6b1de48e641624117766e41b837df691cb5153de4cca3c97fad1b576f705b232 with x2, x3 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying L9.
The subproof is completed by applying H13.
Assume H10: prim1 x3 x0.
Claim L11: ...
...
Claim L12: or (prim1 x3 x2) (prim1 x3 (94f9e.. x2 (λ x4 . (λ x5 . 15418.. x5 (91630.. (4ae4a.. 4a7ef..))) x4)))
...
Apply L12 with prim1 x3 x2 leaving 2 subgoals.
Assume H13: prim1 x3 x2.
The subproof is completed by applying H13.
Assume H13: prim1 x3 (94f9e.. x2 (λ x4 . (λ x5 . 15418.. x5 (91630.. (4ae4a.. 4a7ef..))) x4)).
Apply FalseE with prim1 x3 x2.
Apply unknownprop_9ab9afecf6df9c6c8b7acfacf535da15a80008776d1f4257003609d8ca595ccd with x3, x2 leaving 2 subgoals.
The subproof is completed by applying L9.
The subproof is completed by applying H13.