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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: prim1 x1 (2f2ea.. x0).
Let x2 of type ι be given.
Assume H1: prim1 x2 x1.
Apply unknownprop_7f087020e08fe39f2fb9c18d0d157bca9dcbbd66da68cc2a09c1557f186226cd with x0, x1, prim1 x2 (2f2ea.. x0) leaving 2 subgoals.
The subproof is completed by applying H0.
Let x3 of type ι be given.
Assume H2: ba9d8.. x3.
Assume H3: prim1 x1 (prim0 (aa8d2.. x3 x0)).
Apply unknownprop_901227726ecb21c0c865a7b1769191cd65e10f479fbeb543b259399303379e3e with x0, x2, 4ae4a.. x3 leaving 2 subgoals.
Apply unknownprop_11171438c9340577bc5ca6838eccea0ebdb4279227053bf618ee42741f7851b4 with x3.
The subproof is completed by applying H2.
Apply unknownprop_2e9d54fe36f15d69bc38ced5df919b24525c063654d745631b1351fc65da0131 with x3, x0, λ x4 x5 . prim1 x2 x5 leaving 2 subgoals.
The subproof is completed by applying H2.
Apply UnionI with prim0 (aa8d2.. x3 x0), x2, x1 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H3.