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Proofgold Proof

pf
Apply add_nat_SR with u5, u7, λ x0 x1 . x1 = u13 leaving 2 subgoals.
The subproof is completed by applying nat_7.
set y0 to be ordsucc (add_nat u5 u7)
set y1 to be ordsucc u12
Claim L0: ∀ x2 : ι → ο . x2 y1x2 y0
Let x2 of type ιο be given.
Assume H0: x2 (ordsucc u12).
set y3 to be λ x3 . x2
Apply unknownprop_26eda83e6955cc6e2cd46e060392203cdfb318b5445ce1ce66f9901e9e34123d with λ x4 x5 . y3 (ordsucc x4) (ordsucc x5).
The subproof is completed by applying H0.
Let x2 of type ιιο be given.
Apply L0 with λ x3 . x2 x3 y1x2 y1 x3.
Assume H1: x2 y1 y1.
The subproof is completed by applying H1.