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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Assume H0: 02b90.. x0 x1.
Assume H1: 02b90.. x2 x3.
Assume H2: ∀ x4 . prim1 x4 x0099f3.. x4 (02a50.. x2 x3).
Assume H3: ∀ x4 . prim1 x4 x1099f3.. (02a50.. x2 x3) x4.
Assume H4: ∀ x4 . prim1 x4 x2099f3.. x4 (02a50.. x0 x1).
Assume H5: ∀ x4 . prim1 x4 x3099f3.. (02a50.. x0 x1) x4.
Claim L6: 80242.. (02a50.. x0 x1)
Apply unknownprop_1d872d2fba72bbfb8f4867fe821cad13fefb27fee73f2ea0a29574094d71a01c with x0, x1.
The subproof is completed by applying H0.
Claim L7: 80242.. (02a50.. x2 x3)
Apply unknownprop_1d872d2fba72bbfb8f4867fe821cad13fefb27fee73f2ea0a29574094d71a01c with x2, x3.
The subproof is completed by applying H1.
Apply unknownprop_8a51d0b307e3b4ecc10c81b3620b81438d01c3be1c18ff219f0aae7be6582b4f with 02a50.. x0 x1, 02a50.. x2 x3 leaving 4 subgoals.
The subproof is completed by applying L6.
The subproof is completed by applying L7.
Apply unknownprop_58d169d84431817548b910e1fd0e040562482fe04fdc69328800e0456da1c447 with x0, x1, x2, x3 leaving 4 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 H5.
Apply unknownprop_58d169d84431817548b910e1fd0e040562482fe04fdc69328800e0456da1c447 with x2, x3, x0, x1 leaving 4 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
The subproof is completed by applying H4.
The subproof is completed by applying H3.