Let x0 of type ι be given.

Let x1 of type ι be given.

Let x2 of type ι → ι → ο be given.

Assume H0: x0 = 0fc90.. (4ae4a.. (4ae4a.. 4a7ef..)) (λ x3 . If_i (x3 = 4a7ef..) x1 (d2155.. x1 x2)).

Let x3 of type ι be given.

Assume H1: prim1 x3 x1.

Let x4 of type ι be given.

Assume H2: prim1 x4 x1.

Apply H0 with λ x5 x6 . x2 x3 x4 = 2b2e3.. (f482f.. x6 (4ae4a.. 4a7ef..)) x3 x4.

Apply unknownprop_327f4faff65d2b4b341be7a5ceca39a573a558eea38825726ce72538879f3bc4 with x1, d2155.. x1 x2, λ x5 x6 . x2 x3 x4 = 2b2e3.. x6 x3 x4.

Let x5 of type ο → ο → ο be given.

Apply unknownprop_2f933223abbf06b9432ad394d3d231d453b9216dd478c4e12bd2982ea34a19e5 with x1, x2, x3, x4, λ x6 x7 : ο . x5 x7 x6 leaving 2 subgoals.

The subproof is completed by applying H1.

The subproof is completed by applying H2.

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Proofgold Proof