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Proofgold Proof

pf
Apply unknownprop_85336ee07ace71a942dc508d3b8c851d9d6bb88511443b7dafbf11b71c263f4d with λ x0 . ∀ x1 . prim1 x1 x0ba9d8.. x1 leaving 2 subgoals.
Let x0 of type ι be given.
Assume H0: prim1 x0 4a7ef...
Apply FalseE with ba9d8.. x0.
Apply unknownprop_da3368fefc81e401e6446c98c0c04ab87d76d6f97c47fe5fd07c1e3c2f00ef6a with x0.
The subproof is completed by applying H0.
Let x0 of type ι be given.
Assume H0: ba9d8.. x0.
Assume H1: ∀ x1 . prim1 x1 x0ba9d8.. x1.
Let x1 of type ι be given.
Assume H2: prim1 x1 (4ae4a.. x0).
Apply unknownprop_dec2978c0a72cebd51fcab0a380f03d4d80d1ccd8f826d378953148c305a60f0 with x0, x1, ba9d8.. x1 leaving 3 subgoals.
The subproof is completed by applying H2.
Assume H3: prim1 x1 x0.
Apply H1 with x1.
The subproof is completed by applying H3.
Assume H3: x1 = x0.
Apply H3 with λ x2 x3 . ba9d8.. x3.
The subproof is completed by applying H0.