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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ιι be given.
Apply set_ext with 94f9e.. x0 (λ x2 . x1 x2), a842e.. x0 (λ x2 . 91630.. (x1 x2)) leaving 2 subgoals.
Let x2 of type ι be given.
Assume H0: prim1 x2 (94f9e.. x0 (λ x3 . x1 x3)).
Apply unknownprop_d908b89102f7b662c739e5a844f67efc8ae1cd05a2e9ce1e3546fa3885f40100 with x0, x1, x2, prim1 x2 (a842e.. x0 (λ x3 . 91630.. (x1 x3))) leaving 2 subgoals.
The subproof is completed by applying H0.
Let x3 of type ι be given.
Assume H1: prim1 x3 x0.
Assume H2: x2 = x1 x3.
Apply unknownprop_1a58846f991745a62bb791e57f6ffb9f18f2ca362367c10b2b979fc90a3b62e1 with x0, λ x4 . 91630.. (x1 x4), x3, x2 leaving 2 subgoals.
The subproof is completed by applying H1.
Apply H2 with λ x4 x5 . prim1 x2 (91630.. x4).
The subproof is completed by applying unknownprop_c6d721b795faf1c324094ad380dfe62a3a5dc2ef0b2edf42237be188f6768728 with x2.
Let x2 of type ι be given.
Assume H0: prim1 x2 (a842e.. x0 (λ x3 . 91630.. (x1 x3))).
Apply unknownprop_6e713ef2b1c9d2089dead8e3d98fed6bda91ffc6b807ed8732c89724a15f5c2c with x0, λ x3 . 91630.. (x1 x3), x2, prim1 x2 (94f9e.. x0 (λ x3 . x1 x3)) leaving 2 subgoals.
The subproof is completed by applying H0.
Let x3 of type ι be given.
Assume H1: and (prim1 x3 x0) (prim1 x2 (91630.. (x1 x3))).
Apply H1 with prim1 x2 (94f9e.. x0 (λ x4 . x1 x4)).
Assume H2: prim1 x3 x0.
Assume H3: prim1 x2 (91630.. (x1 x3)).
Claim L4: x2 = x1 x3
Apply unknownprop_30833a9978e304b25ffd59c347245315985872140acc9e441a97543a28184d79 with x1 x3, x2.
The subproof is completed by applying H3.
Apply L4 with λ x4 x5 . prim1 x5 (94f9e.. x0 (λ x6 . x1 x6)).
Apply unknownprop_4785a7374559bd7d78314ce01f76cab97234c9b29cfa5b01c939c64f8ccf18e4 with x0, x1, x3.
The subproof is completed by applying H2.