Let z be given.
Assume Hz.
We prove the intermediate claim Lp0z: F (proj0 z).
An
exact proof term for the current goal is
CD_proj0R z Hz.
We prove the intermediate claim Lp1z: F (proj1 z).
An
exact proof term for the current goal is
CD_proj1R z Hz.
We will
prove pa (proj0 z + proj0 0) (proj1 z + proj1 0) = z.
rewrite the current goal using
CD_proj0_F F_0 0 F_0 (from left to right).
rewrite the current goal using
CD_proj1_F F_0 0 F_0 (from left to right).
rewrite the current goal using F_add_0R (proj0 z) ?? (from left to right).
rewrite the current goal using F_add_0R (proj1 z) ?? (from left to right).
We will prove pa (proj0 z) (proj1 z) = z.
Use symmetry.
∎