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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: 80242.. x0.
Assume H1: 80242.. x1.
Let x2 of type ι be given.
Assume H2: prim1 x2 x0.
Let x3 of type ι be given.
Assume H3: prim1 x3 x1.
Assume H4: (λ x4 . 15418.. x4 (91630.. (4ae4a.. (4ae4a.. 4a7ef..)))) x2 = (λ x4 . 15418.. x4 (91630.. (4ae4a.. (4ae4a.. 4a7ef..)))) x3.
Let x4 of type ι be given.
Assume H5: prim1 x4 x2.
Claim L6: prim1 x4 ((λ x5 . 15418.. x5 (91630.. (4ae4a.. (4ae4a.. 4a7ef..)))) x3)
Apply H4 with λ x5 x6 . prim1 ... ....
...
Apply unknownprop_b46721c187c37140cbae22d356b00ba89f4126d81d8665e4be15b5a58c78d06f with x3, 91630.. (91630.. (4ae4a.. (4ae4a.. 4a7ef..))), x4, prim1 x4 x3 leaving 3 subgoals.
The subproof is completed by applying L6.
Assume H7: prim1 x4 x3.
The subproof is completed by applying H7.
Assume H7: prim1 x4 (91630.. (91630.. (4ae4a.. (4ae4a.. 4a7ef..)))).
Apply FalseE with prim1 x4 x3.
Claim L8: x4 = 91630.. (4ae4a.. (4ae4a.. 4a7ef..))
Apply unknownprop_30833a9978e304b25ffd59c347245315985872140acc9e441a97543a28184d79 with 91630.. (4ae4a.. (4ae4a.. 4a7ef..)), x4.
The subproof is completed by applying H7.
Claim L9: prim1 (91630.. (4ae4a.. (4ae4a.. 4a7ef..))) x2
Apply L8 with λ x5 x6 . prim1 x5 x2.
The subproof is completed by applying H5.
Apply H0 with False.
Let x5 of type ι be given.
Assume H10: (λ x6 . and (ordinal x6) (1beb9.. x6 x0)) x5.
Apply H10 with False.
Assume H11: ordinal x5.
Assume H12: 1beb9.. x5 x0.
Apply H12 with False.
Assume H13: Subq x0 (472ec.. x5).
Apply FalseE with (∀ x6 . prim1 x6 x5 ⟶ exactly1of2 (prim1 (15418.. x6 (91630.. (4ae4a.. 4a7ef..))) x0) (prim1 x6 x0)) ⟶ False.
Apply unknownprop_b46721c187c37140cbae22d356b00ba89f4126d81d8665e4be15b5a58c78d06f with x5, 94f9e.. x5 (λ x6 . (λ x7 . 15418.. x7 (91630.. (4ae4a.. 4a7ef..))) x6), x2, False leaving 3 subgoals.
Apply H13 with x2.
The subproof is completed by applying H2.
Assume H14: prim1 x2 x5.
Claim L15: ordinal x2
Apply ordinal_Hered with x5, x2 leaving 2 subgoals.
The subproof is completed by applying H11.
The subproof is completed by applying H14.
Apply unknownprop_233a01ed74afb32f65afd3e8784abd0a97273e5d2c2787b08adfb08e640439ec.
Apply ordinal_Hered with x2, 91630.. (4ae4a.. (4ae4a.. 4a7ef..)) leaving 2 subgoals.
The subproof is completed by applying L15.
The subproof is completed by applying L9.
Assume H14: prim1 x2 (94f9e.. x5 (λ x6 . (λ x7 . 15418.. x7 (91630.. (4ae4a.. 4a7ef..))) x6)).
Apply unknownprop_d908b89102f7b662c739e5a844f67efc8ae1cd05a2e9ce1e3546fa3885f40100 with x5, λ x6 . (λ x7 . 15418.. x7 (91630.. (4ae4a.. 4a7ef..))) x6, x2, False leaving 2 subgoals.
The subproof is completed by applying H14.
Let x6 of type ι be given.
Assume H15: prim1 x6 x5.
Assume H16: x2 = (λ x7 . 15418.. x7 (91630.. (4ae4a.. 4a7ef..))) x6.
Claim L17: ordinal x6
Apply ordinal_Hered with x5, x6 leaving 2 subgoals.
The subproof is completed by applying H11.
The subproof is completed by applying H15.
Claim L18: prim1 (91630.. (4ae4a.. (4ae4a.. 4a7ef..))) ((λ x7 . 15418.. x7 (91630.. (4ae4a.. 4a7ef..))) x6)
Apply H16 with λ x7 x8 . prim1 (91630.. (4ae4a.. (4ae4a.. 4a7ef..))) x7.
The subproof is completed by applying L9.
Apply unknownprop_b46721c187c37140cbae22d356b00ba89f4126d81d8665e4be15b5a58c78d06f with x6, 91630.. (91630.. (4ae4a.. 4a7ef..)), 91630.. (4ae4a.. (4ae4a.. 4a7ef..)), False leaving 3 subgoals.
The subproof is completed by applying L18.
Assume H19: prim1 (91630.. (4ae4a.. (4ae4a.. 4a7ef..))) x6.
Apply unknownprop_233a01ed74afb32f65afd3e8784abd0a97273e5d2c2787b08adfb08e640439ec.
Apply ordinal_Hered with x6, 91630.. (4ae4a.. (4ae4a.. 4a7ef..)) leaving 2 subgoals.
The subproof is completed by applying L17.
The subproof is completed by applying H19.
The subproof is completed by applying unknownprop_e87260b1013ba25c00e71f0b980f91b6ef632a8abaf76671d652722aaa34ef37.
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