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Proofgold Proof

pf
Let x0 of type ι → ο be given.
Assume H0: ∀ x1 . 80242.. x1 ⟶ (∀ x2 . prim1 x2 (56ded.. (e4431.. x1)) ⟶ x0 x2) ⟶ x0 x1.
Claim L1: ∀ x1 . ordinal x1 ⟶ ∀ x2 . prim1 x2 (56ded.. x1) ⟶ x0 x2
Apply ordinal_ind with λ x1 . ∀ x2 . prim1 x2 (56ded.. x1) ⟶ x0 x2.
Let x1 of type ι be given.
Assume H1: ordinal x1.
Assume H2: ∀ x2 . prim1 x2 x1 ⟶ ∀ x3 . prim1 x3 (56ded.. x2) ⟶ x0 x3.
Let x2 of type ι be given.
Assume H3: prim1 x2 (56ded.. x1).
Apply unknownprop_cd21c13b2c3f5b1a3b98367fcb2ef0b03b319d8c325362ea48d721c1e2e4842f with x1, x2, x0 x2 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
Assume H4: prim1 (e4431.. x2) x1.
Assume H5: ordinal (e4431.. x2).
Assume H6: 80242.. x2.
Assume H7: 1beb9.. (e4431.. x2) x2.
Apply H0 with x2 leaving 2 subgoals.
The subproof is completed by applying H6.
Apply H2 with e4431.. x2.
The subproof is completed by applying H4.
Apply unknownprop_6c83aea55248a32d2f62fb7ccc815ac2dd05de38825f10675c578219708d279b with x0.
The subproof is completed by applying L1.
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