Apply unknownprop_1db1571afe8c01990252b7801041a0001ba1fedff9d78947d027d61a0ff0ae7f with λ x0 . x0 ∈ prim6 0, λ x0 . x0, HomSet leaving 3 subgoals.

Let x0 of type ι be given.

Let x1 of type ι be given.

Let x2 of type ι be given.

Assume H0: x0 ∈ prim6 0.

Assume H1: x1 ∈ prim6 0.

Assume H2: HomSet x0 x1 x2.

The subproof is completed by applying H2.

Let x0 of type ι be given.

Assume H0: x0 ∈ prim6 0.

The subproof is completed by applying lam_id_exp_In with x0.

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.

Let x4 of type ι be given.

Assume H0: x0 ∈ prim6 0.

Assume H1: x1 ∈ prim6 0.

Assume H2: x2 ∈ prim6 0.

Assume H3: HomSet x0 x1 x3.

Assume H4: HomSet x1 x2 x4.

Apply lam_comp_exp_In with x0, x1, x2, x3, x4 leaving 2 subgoals.

The subproof is completed by applying H3.

The subproof is completed by applying H4.

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Proofgold Proof