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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: atleastp (setsum x0 x1) x0.
Apply unknownprop_4bfbb4dec5e67ad21ca2193ea2b4908e823372bc7bdc402dd93e056c69cdf1ed with setsum x0 x1, x0, x1 = 0 leaving 2 subgoals.
The subproof is completed by applying H0.
Let x2 of type ι be given.
Assume H1: (λ x3 . and (Subq x3 x0) (equip (setsum x0 x1) x3)) x2.
Apply andE with Subq x2 x0, equip (setsum x0 x1) x2, x1 = 0 leaving 2 subgoals.
The subproof is completed by applying H1.
Assume H2: Subq x2 x0.
Assume H3: equip (setsum x0 x1) x2.
Claim L4: setsum (setminus x0 x2) x1 = 0
Apply unknownprop_2930a4208854e6b6adcdb51a7c34faf7a8789ce5177dbf41617428ceaf9b3c6b with x2, setsum (setminus x0 x2) x1.
Apply unknownprop_01b7f7993ff222473c0dc551f861729864a2fa847d49dc4751edad0602198144 with setsum x2 (setsum (setminus x0 x2) x1), setsum (setsum x2 (setminus x0 x2)) x1, x2 leaving 2 subgoals.
Apply unknownprop_1b764290fde7c6be5dad24a6a257b6d0c773613bb687261020b529743ed07853 with setsum (setsum x2 (setminus x0 x2)) x1, setsum x2 (setsum (setminus x0 x2) x1).
The subproof is completed by applying unknownprop_766395d00d5702634c7092b386cd74ca5b8819cfa7c5b44f21fdf51440a1519d with x2, setminus x0 x2, x1.
Apply unknownprop_01b7f7993ff222473c0dc551f861729864a2fa847d49dc4751edad0602198144 with setsum (setsum x2 (setminus x0 x2)) x1, setsum x0 x1, x2 leaving 2 subgoals.
Apply unknownprop_092a01ae1d0b9a6545cd8d7970276c4297444af2ad61da23593151943992d677 with setsum x2 (setminus x0 x2), x1, x0, x1 leaving 2 subgoals.
Apply unknownprop_90a352f74f9892bfc39c1ccdaecae19d23018050a6f899381839d73f3a3293bc with x0, x2.
The subproof is completed by applying H2.
The subproof is completed by applying unknownprop_779bad135e02b130c4f2c6fb2f6a4cc60941e04327d78e3212c24d54199ba5e5 with x1.
The subproof is completed by applying H3.
Apply unknownprop_fe7ff313be3d0b9f2334c12982636aff94f7603137e8053506a95c79965309c2 with x1.
Let x3 of type ι be given.
Apply unknownprop_b30a94f49240f0717f4ecb200a605aa8a4e6dad6dc5d1afa60c37866ee96baab with x3, x1.
Assume H5: In x3 x1.
Apply unknownprop_1cc88f7e87aaf8c5cee24b4a69ff535a81e7855c45a9fd971eec05ee4cc28f9c with Inj1 x3.
Apply L4 with λ x4 x5 . In (Inj1 x3) x4.
Apply unknownprop_509aadde20bd8e655e679e36fea278577d08a1dbe475eed73f3fccc8c2d65f15 with setminus x0 x2, x1, x3.
The subproof is completed by applying H5.