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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι → ι → ο be given.
Assume H0: ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ x1 x2 x3 ⟶ x1 x3 x2.
Assume H1: 4402e.. x0 x1.
Assume H2: cf2df.. x0 x1.
Let x2 of type ι be given.
Assume H3: x2 ∈ x0.
Let x3 of type ι be given.
Assume H4: x3 ⊆ setminus x0 (Sing x2).
Assume H5: 41e30.. x3 x1.
Apply H5 with 5bab1.. x0 x1 leaving 12 subgoals.
Apply unknownprop_346f3bbbcc5cde59e868dc0e1e982e254616a3f230daa12c2d422cd6752db064 with x0, x1, x2, x3 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply unknownprop_c099cf5597229c344fa36d9d78ba8d94d2e8b63679655baa0ee0abf6c6f9dc70 with x0, x1, x2, x3 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply unknownprop_6158c7d567814903e16f78f2fe31aa614ce164da41b73bf44c5273da45a97118 with x0, x1, x2, x3 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply unknownprop_4289293283b08836b9bd2abd59b8474569b48923f5d7f85fbb7873b47030480c with x0, x1, x2, x3 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply unknownprop_00e5c06e7db48ad99a033b3dfcafe7652d38dec0249dfd23b792ff21572e629c with x0, x1, x2, x3 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply unknownprop_9f092eb4f8fccc9fec331bc349425ee9ee5a43d5bdc7204ce471536c72bde810 with x0, x1, x2, x3 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply unknownprop_4ff26f98210102e077b11c44a84537a8ec57b8c9f628e188dea8287bb5189c4c with x0, x1, x2, x3 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply unknownprop_46ada203bfa7ad8d6b0132736e99f6e3194274a8dd402432aabb1da27f25f826 with x0, x1, x2, x3 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply unknownprop_e29efafc72fbe9fe513474a4ea220336dbb92ba94b5559ab1ddbb01246fe041d with x0, x1, x2, x3 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply unknownprop_d2bc614fed641e77a3100bdfb435ea4ad16c82c8e5e7b30e76eda4e6dac6755f with x0, x1, x2, x3 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply unknownprop_4e004ea5da57b5fc70a86184b5f6e143a20ad1ef57e4ffca59aaf8ac3e0e80e8 with x0, x1, x2, x3 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply unknownprop_280c184d9753d504e49cad1f2996f46934063cdf61157816e7c1f0d6854357de with x0, x1, x2, x3 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
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