Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
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.
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.