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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: b45a2.. x3 x1.
Apply H5 with 5bab1.. x0 x1 leaving 12 subgoals.
Apply unknownprop_2b0a9a61f3bf2251a2ca11d341a668f88e9044d7efaa0bd1557fa6015d7c0b39 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_55fb81c2255657a8a15b8ebf2d76179a23a8d61fbb4b642d287e4f9e57d7f3c0 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_3cf1b4d63ffa97c570a31d3fc1201ac8228ce55e97b64b5e07d910608ca7c24d 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_5663fe7922f65c5d33bb45030018c36c5cbcb4a20b316bd4f71014a9ae88caf3 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_9ff9795957901549df9f1d022ea52a8bd49ac61010d2f49e00394822414ae93d 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_0bcf4a357652dbdff8581d9574f07fe4f37cf545492504b62164883e082fa101 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_16a21346d950ddd35f5b1906c32ea1a9ddd68ae4bb827996d0a6edef0ad0901c 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_fd863d45d56dda7fd80d751fe171b3f5163b9342ee26a6320f781e78c9a41848 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_102cd5b2db0a3b02383d2c753dbfd1921fba26dda0b0f35d5664afaa67461431 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_9e964db177f1a7205fb11e02a3136802ae65dcf8cfe9de61ac81c8db08a04a7b 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_15d2d63b47e168f740a0e4827395e4b0ef861008c57fe53a1005536840a77a60 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_36ec408517035173348e96e80aa721612a56ddd18d2f139569000db5e49a6088 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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