Let x0 of type ι be given.

Let x1 of type ι be given.

Let x2 of type ι → ο be given.

Assume H0: x0 = 0fc90.. (4ae4a.. (4ae4a.. 4a7ef..)) (λ x3 . If_i (x3 = 4a7ef..) x1 (1216a.. x1 x2)).

Let x3 of type ι be given.

Assume H1: prim1 x3 x1.

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

Apply unknownprop_327f4faff65d2b4b341be7a5ceca39a573a558eea38825726ce72538879f3bc4 with x1, 1216a.. x1 x2, λ x4 x5 . x2 x3 = decode_p x5 x3.

Let x4 of type ο → ο → ο be given.

Apply unknownprop_ffe6e40960e279c2bfdd5436564fb47b3416a2f4b47c7977262e0b5dc7ec2541 with x1, x2, x3, λ x5 x6 : ο . x4 x6 x5.

The subproof is completed by applying H1.

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Proofgold Proof