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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: ordinal x0.
Let x1 of type ι → ο be given.
Apply andI with Subq (09072.. x0 x1) (472ec.. x0), ∀ x2 . prim1 x2 x0 ⟶ exactly1of2 (prim1 ((λ x3 . 15418.. x3 (91630.. (4ae4a.. 4a7ef..))) x2) (09072.. x0 x1)) (prim1 x2 (09072.. x0 x1)) leaving 2 subgoals.
Let x2 of type ι be given.
Assume H1: prim1 x2 (09072.. x0 x1).
Apply unknownprop_b46721c187c37140cbae22d356b00ba89f4126d81d8665e4be15b5a58c78d06f with 1216a.. x0 (λ x3 . x1 x3), a4c2a.. x0 (λ x3 . not (x1 x3)) (λ x3 . (λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3), x2, prim1 x2 (472ec.. x0) leaving 3 subgoals.
The subproof is completed by applying H1.
Assume H2: prim1 x2 (1216a.. x0 (λ x3 . x1 x3)).
Apply unknownprop_e4362c04e65a765de9cf61045b78be0adc0f9e51a17754420e1088df0891ff67 with x0, x1, x2, prim1 x2 (472ec.. x0) leaving 2 subgoals.
The subproof is completed by applying H2.
Assume H3: prim1 x2 x0.
Assume H4: x1 x2.
Apply unknownprop_0b5b61a66a1ed2eb843dbce5c5f6930c63a284fe5e33704d9f0cc564310ec40b with x0, 94f9e.. x0 (λ x3 . (λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3), x2.
The subproof is completed by applying H3.
Assume H2: prim1 x2 (a4c2a.. x0 (λ x3 . not (x1 x3)) (λ x3 . (λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3)).
Apply unknownprop_e546e9a8cc28c7314a8604ada98e2a83641f2ef6b8078441570ffe037b28d26f with x0, λ x3 . not (x1 x3), λ x3 . (λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3, x2, prim1 x2 (472ec.. x0) leaving 2 subgoals.
The subproof is completed by applying H2.
Let x3 of type ι be given.
Assume H3: prim1 x3 x0.
Assume H4: not (x1 x3).
Assume H5: x2 = (λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3.
Apply unknownprop_e4d6e0bfb4ef6d52ee13edd54a77c8cc7f0a3af8ffb1b8da66d4f98842dd28b5 with x0, 94f9e.. x0 (λ x4 . (λ x5 . 15418.. x5 (91630.. (4ae4a.. 4a7ef..))) x4), x2.
Apply H5 with λ x4 x5 . prim1 x5 (94f9e.. x0 (λ x6 . (λ x7 . 15418.. x7 (91630.. (4ae4a.. 4a7ef..))) x6)).
Apply unknownprop_4785a7374559bd7d78314ce01f76cab97234c9b29cfa5b01c939c64f8ccf18e4 with x0, λ x4 . (λ x5 . 15418.. x5 (91630.. (4ae4a.. 4a7ef..))) x4, x3.
The subproof is completed by applying H3.
Let x2 of type ι be given.
Assume H1: prim1 x2 x0.
Claim L2: ...
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Apply xm with x1 x2, exactly1of2 (prim1 ((λ x3 . 15418.. x3 (91630.. (4ae4a.. 4a7ef..))) x2) (09072.. x0 x1)) (prim1 x2 (09072.. x0 x1)) leaving 2 subgoals.
Assume H3: x1 x2.
Apply exactly1of2_I2 with prim1 ((λ x3 . 15418.. x3 (91630.. (4ae4a.. 4a7ef..))) x2) (09072.. x0 x1), prim1 x2 (09072.. x0 x1) leaving 2 subgoals.
Assume H4: prim1 ((λ x3 . 15418.. x3 (91630.. (4ae4a.. 4a7ef..))) x2) (09072.. x0 x1).
Apply unknownprop_b46721c187c37140cbae22d356b00ba89f4126d81d8665e4be15b5a58c78d06f with 1216a.. x0 (λ x3 . x1 x3), a4c2a.. x0 (λ x3 . not (x1 x3)) (λ x3 . (λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3), (λ x3 . 15418.. ... ...) ..., ... leaving 3 subgoals.
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