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Proofgold Proof

pf
Apply add_nat_SR with u31, 25, λ x0 x1 . x1 = u57 leaving 2 subgoals.
The subproof is completed by applying unknownprop_12d4f070cde272005208a956be7c68072a214891c891a748c20b9d965edfb16c.
set y0 to be ordsucc (add_nat u31 u25)
set y1 to be ordsucc u56
Claim L0: ∀ x2 : ι → ο . x2 y1 ⟶ x2 y0
Let x2 of type ι → ο be given.
Assume H0: x2 (ordsucc u56).
set y3 to be λ x3 . x2
Apply unknownprop_3957b61b0a55afc2bf57e4dc91793f98b65c01d301159bc661e37ae5d33fd811 with λ x4 x5 . y3 (ordsucc x4) (ordsucc x5).
The subproof is completed by applying H0.
Let x2 of type ι → ι → ο be given.
Apply L0 with λ x3 . x2 x3 y1 ⟶ x2 y1 x3.
Assume H1: x2 y1 y1.
The subproof is completed by applying H1.
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