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Proofgold Proof

pf
Apply unknownprop_3d492f63bbda05786f59e1a020a0f00cded12b012672cfcb59b4dfe595a76487 with ordsucc, nat_p, λ x0 . add_nat 41 x0, ChurchNum_ii_3 ChurchNum2 ordsucc 1, λ x0 x1 . x1 = 82 leaving 4 subgoals.
The subproof is completed by applying nat_ordsucc.
The subproof is completed by applying add_nat_SR with 41.
The subproof is completed by applying nat_9.
Apply unknownprop_e2cb0de7874d400d74b6cb5cf619af6f48ae813f369fbf388b00f41ca04e606a with ordsucc, nat_p, λ x0 . add_nat 41 x0, 1, λ x0 x1 . ChurchNum_ii_5 ChurchNum2 ordsucc x1 = 82 leaving 4 subgoals.
The subproof is completed by applying nat_ordsucc.
The subproof is completed by applying add_nat_SR with 41.
The subproof is completed by applying nat_1.
Apply add_nat_SR with 41, 0, λ x0 x1 . ChurchNum_ii_5 ChurchNum2 ordsucc (ChurchNum_ii_3 ChurchNum2 ordsucc x1) = 82 leaving 2 subgoals.
The subproof is completed by applying nat_0.
Apply add_nat_0R with 41, λ x0 x1 . ChurchNum_ii_5 ChurchNum2 ordsucc (ChurchNum_ii_3 ChurchNum2 ordsucc (ordsucc x1)) = 82.
Let x0 of type ι → ι → ο be given.
Assume H0: x0 (ChurchNum_ii_5 ChurchNum2 ordsucc (ChurchNum_ii_3 ChurchNum2 ordsucc 42)) 82.
The subproof is completed by applying H0.
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