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Proofgold Proof

pf
Let x0 of type ι be given.
Apply set_ext with e5b72.. (91630.. x0), prim2 4a7ef.. (91630.. x0) leaving 2 subgoals.
Let x1 of type ι be given.
Assume H0: prim1 x1 (e5b72.. (91630.. x0)).
Apply xm with prim1 x0 x1, prim1 x1 (prim2 4a7ef.. (91630.. x0)) leaving 2 subgoals.
Assume H1: prim1 x0 x1.
Claim L2: x1 = 91630.. x0
Apply set_ext with x1, 91630.. x0 leaving 2 subgoals.
Apply unknownprop_4134b8a5d866cd7ad711ea569ada0ca0ba949f5cad571bf5782dc7c2d15cdb1c with 91630.. x0, x1.
The subproof is completed by applying H0.
Let x2 of type ι be given.
Assume H2: prim1 x2 (91630.. x0).
Apply unknownprop_30833a9978e304b25ffd59c347245315985872140acc9e441a97543a28184d79 with x0, x2, λ x3 x4 . prim1 x4 x1 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H1.
Apply L2 with λ x2 x3 . prim1 x3 (prim2 4a7ef.. (91630.. x0)).
The subproof is completed by applying unknownprop_70f06371245ce38fbbca963cb4d7e422ccf350d2e27735c617635b09cbcba701 with 4a7ef.., 91630.. x0.
Assume H1: nIn x0 x1.
Claim L2: x1 = 4a7ef..
Apply unknownprop_fa66e3d1737b2c05fa4008399b4c740ee88bf9334c6b435957b41684dfedfe51 with x1.
Let x2 of type ι be given.
Assume H2: prim1 x2 x1.
Claim L3: prim1 x2 (91630.. x0)
Apply unknownprop_4134b8a5d866cd7ad711ea569ada0ca0ba949f5cad571bf5782dc7c2d15cdb1c with 91630.. x0, x1, x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
Claim L4: x2 = x0
Apply unknownprop_30833a9978e304b25ffd59c347245315985872140acc9e441a97543a28184d79 with x0, x2.
The subproof is completed by applying L3.
Apply H1.
Apply L4 with λ x3 x4 . prim1 x3 x1.
The subproof is completed by applying H2.
Apply L2 with λ x2 x3 . prim1 x3 (prim2 4a7ef.. (91630.. x0)).
The subproof is completed by applying unknownprop_893870ab8a49d622c10a8fe954eea30d7bd2b94aa27e9c6b21eab85a9f81d115 with 4a7ef.., 91630.. x0.
Let x1 of type ι be given.
Assume H0: prim1 x1 (prim2 4a7ef.. (91630.. x0)).
Apply unknownprop_44132e34b8fcc92e54ff875d0e8f6137eeea7d41bb9d4b117dbbbb4d2f239782 with x1, 4a7ef.., 91630.. x0, prim1 x1 (e5b72.. (91630.. x0)) leaving 3 subgoals.
The subproof is completed by applying H0.
Assume H1: x1 = 4a7ef...
Apply H1 with λ x2 x3 . prim1 x3 (e5b72.. (91630.. x0)).
The subproof is completed by applying unknownprop_21eccfc5b947b8f10314dfc0734b94272c3a79b52ca9a3c84823212c3425dcb8 with 91630.. x0.
Assume H1: x1 = 91630.. x0.
Apply H1 with λ x2 x3 . prim1 x3 (e5b72.. (91630.. x0)).
The subproof is completed by applying unknownprop_1b39b6239e12488e23a0cc3dcb046ad70d13f361e325cf6f0925987c38e98e86 with 91630.. x0.