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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: prim1 x1 (a4c2a.. x0 (λ x2 . ∃ x3 . f6917.. x3 = x2) (λ x2 . 158d3.. x2)).
Apply unknownprop_669df0da86db4f986bae532f93288cb46feb5b77310c7f6de7766507585de4c6 with λ x2 x3 : ι → ι . prim1 (x2 x1) x0.
Apply unknownprop_e546e9a8cc28c7314a8604ada98e2a83641f2ef6b8078441570ffe037b28d26f with x0, λ x2 . ∃ x3 . f6917.. x3 = x2, 158d3.., x1, prim1 (f6917.. x1) x0 leaving 2 subgoals.
The subproof is completed by applying H0.
Let x2 of type ι be given.
Assume H1: prim1 x2 x0.
Assume H2: ∃ x3 . f6917.. x3 = x2.
Assume H3: x1 = 158d3.. x2.
Apply H2 with prim1 (f6917.. x1) x0.
Let x3 of type ι be given.
Assume H4: f6917.. x3 = x2.
Apply H3 with λ x4 x5 . prim1 (f6917.. x5) x0.
Apply H4 with λ x4 x5 . prim1 (f6917.. (158d3.. x4)) x0.
Apply unknownprop_31dc82295b7aa4a340f2278c1cf4aa729add061fe389e3a99b659752ce7d8635 with x3, λ x4 x5 . prim1 (f6917.. x5) x0.
Apply H4 with λ x4 x5 . prim1 x5 x0.
The subproof is completed by applying H1.
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