Section STABILITY.
Variables env env': composite_env.
Hypothesis extends: forall id co, env!id = Some co -> env'!id = Some co.
End STABILITY.

Lemma add_composite_definitions_incr:
forall id co defs env1 env2,
add_composite_definitions env1 defs = OK env2 ->
env1!id = Some co -> env2!id = Some co.