Claim L0: ∀ x0 x1 x2 x3 . struct_p x0 ⟶ struct_p x1 ⟶ UnaryPredHom x0 x1 x2 ⟶ UnaryPredHom x0 x1 x3 ⟶ struct_p (2d9d0.. x0 x1 x2 x3)

Let x0 of type ι be given.

Let x1 of type ι be given.

Let x2 of type ι be given.

Let x3 of type ι be given.

Assume H0: struct_p x0.

Assume H1: struct_p x1.

Assume H2: UnaryPredHom x0 x1 x2.

Assume H3: UnaryPredHom x0 x1 x3.

Apply H0 with λ x4 . struct_p (2d9d0.. x4 x1 x2 x3).

Let x4 of type ι be given.

Let x5 of type ι → ο be given.

Apply unknownprop_ff02229be25df4b054a60f80e6ec97989fbf3c3db5512351c69dd5b93da7c7d8 with x4, x5, x1, x2, x3, λ x6 x7 . struct_p x7.

The subproof is completed by applying pack_struct_p_I with {x6 ∈ x4|ap x2 x6 = ap x3 x6}, x5.

Apply unknownprop_81d5b76d54c329b7fe3f511000dac691b135e711b748a3d1f0b5a7034428ac1f with struct_p leaving 2 subgoals.

Let x0 of type ι be given.

Assume H1: struct_p x0.

The subproof is completed by applying H1.

The subproof is completed by applying L0.

■

Proofgold Proof