Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι be given.
Let x3 of type ι → ι be given.
Assume H0:
∀ x4 . prim1 x4 x0 ⟶ Subq (x2 x4) (x3 x4).
Apply Subq_tra with
3097a.. x0 (λ x4 . x2 x4),
3097a.. x0 (λ x4 . x3 x4),
3097a.. x1 (λ x4 . x3 x4) leaving 2 subgoals.
Apply unknownprop_bda11531b62ad3d70d98a80cf6a285c14c05b27a16bc3fa17a1a7b75ba77ecfc with
x0,
x2,
x3.
The subproof is completed by applying H0.
Apply unknownprop_1a4eea2e7e2053f757a088192061db01d519464057770f62e2fa414ed5ef28ac with
x0,
x1,
x3 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.