Definition z_op_beq a b : bool :=
match a, b with
| fZ_lt, fZ_lt
| fZ_le, fZ_le
| fZ_gt, fZ_gt
| fZ_ge, fZ_ge
| fZ_add, fZ_add
| fZ_sub, fZ_sub
| fZ_mul, fZ_mul
| fZ_div, fZ_div
| fZ_mod, fZ_mod
| fZ_land, fZ_land
| fZ_max, fZ_max
| fZ_opp, fZ_opp  => true
| _, _ => false
end.

Lemma z_op_beq_sound : forall a b, z_op_beq a b = true -> a = b.