Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Let x2 of type ι → ι → ο be given.
Let x3 of type ι be given.
Let x4 of type ι be given.
Assume H1:
prim1 x4 (x1 x3).
Assume H2: x2 x3 x4.
Apply unknownprop_1dada0fb38ff7f9b45b564ad11d6295d93250427446875218f17ee62431454a6 with
0fc90.. x0 (λ x5 . x1 x5),
λ x5 . x2 (f482f.. x5 4a7ef..) (f482f.. x5 (4ae4a.. 4a7ef..)),
0fc90.. (4ae4a.. (4ae4a.. 4a7ef..)) (λ x5 . If_i (x5 = 4a7ef..) x3 x4) leaving 2 subgoals.
Apply unknownprop_19a146fddf3209a9cb9037b3c55d31c340ac02a53a93d51ec1e8262af3504478 with
x0,
λ x5 . x1 x5,
x3,
x4 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply unknownprop_67d8fddea88125b50903f4bd482ed1753cb719c67016df79894ab3055421315b with
x3,
x4,
λ x5 x6 . x2 x6 (f482f.. (0fc90.. (4ae4a.. (4ae4a.. 4a7ef..)) (λ x7 . If_i (x7 = 4a7ef..) x3 x4)) (4ae4a.. 4a7ef..)).
Apply unknownprop_327f4faff65d2b4b341be7a5ceca39a573a558eea38825726ce72538879f3bc4 with
x3,
x4,
λ x5 x6 . x2 x3 x6.
The subproof is completed by applying H2.