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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: ordinal x0.
Apply xm with ∃ x1 . and (prim1 x1 x0) (x0 = 4ae4a.. x1), or (∀ x1 . prim1 x1 x0 ⟶ prim1 (4ae4a.. x1) x0) (∃ x1 . and (prim1 x1 x0) (x0 = 4ae4a.. x1)) leaving 2 subgoals.
Assume H1: ∃ x1 . and (prim1 x1 x0) (x0 = 4ae4a.. x1).
Apply orIR with ∀ x1 . prim1 x1 x0 ⟶ prim1 (4ae4a.. x1) x0, ∃ x1 . and (prim1 x1 x0) (x0 = 4ae4a.. x1).
The subproof is completed by applying H1.
Assume H1: not (∃ x1 . and (prim1 x1 x0) (x0 = 4ae4a.. x1)).
Apply orIL with ∀ x1 . prim1 x1 x0 ⟶ prim1 (4ae4a.. x1) x0, ∃ x1 . and (prim1 x1 x0) (x0 = 4ae4a.. x1).
Let x1 of type ι be given.
Assume H2: prim1 x1 x0.
Apply unknownprop_be250f85f3dffbb916064f41a6351d4768b4e417d7e89dc1e1bbd4f0f22c18a7 with x0, x1, prim1 (4ae4a.. x1) x0 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
Assume H3: prim1 (4ae4a.. x1) x0.
The subproof is completed by applying H3.
Assume H3: x0 = 4ae4a.. x1.
Apply FalseE with prim1 (4ae4a.. x1) x0.
Apply H1.
Let x2 of type ο be given.
Assume H4: ∀ x3 . and (prim1 x3 x0) (x0 = 4ae4a.. x3) ⟶ x2.
Apply H4 with x1.
Apply andI with prim1 x1 x0, x0 = 4ae4a.. x1 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
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