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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: ba9d8.. x0.
Apply H0 with λ x1 . ∀ x2 . prim1 x2 x1 ⟶ prim1 (4ae4a.. x2) (4ae4a.. x1) leaving 2 subgoals.
Let x1 of type ι be given.
Assume H1: prim1 x1 4a7ef...
Apply FalseE with prim1 (4ae4a.. x1) (4ae4a.. 4a7ef..).
Apply unknownprop_da3368fefc81e401e6446c98c0c04ab87d76d6f97c47fe5fd07c1e3c2f00ef6a with x1.
The subproof is completed by applying H1.
Let x1 of type ι be given.
Assume H1: ∀ x2 . prim1 x2 x1 ⟶ prim1 (4ae4a.. x2) (4ae4a.. x1).
Let x2 of type ι be given.
Assume H2: prim1 x2 (4ae4a.. x1).
Apply unknownprop_dec2978c0a72cebd51fcab0a380f03d4d80d1ccd8f826d378953148c305a60f0 with x1, x2, prim1 (4ae4a.. x2) (4ae4a.. (4ae4a.. x1)) leaving 3 subgoals.
The subproof is completed by applying H2.
Assume H3: prim1 x2 x1.
Claim L4: prim1 (4ae4a.. x2) (4ae4a.. x1)
Apply H1 with x2.
The subproof is completed by applying H3.
Apply unknownprop_4c4b27a97d7f3e81d4abb7629b850d6c55c186f55f30e3dfae132a3ddf1e0a30 with 4ae4a.. x1, 4ae4a.. x2.
The subproof is completed by applying L4.
Assume H3: x2 = x1.
Apply H3 with λ x3 x4 . prim1 (4ae4a.. x4) (4ae4a.. (4ae4a.. x1)).
The subproof is completed by applying unknownprop_38ce50d6b52a0a920b530e7796207ec902a42d65414467df1ecd3efb123f4cb9 with 4ae4a.. x1.
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