Section ILogicEmbedFacts.
Context {A B} `{HAB: Embed A B} {ILA: ILogic A} {ILB: ILogic B}.
Global Instance embed_lentails_m :
Proper (lentails ==> lentails) embed.
Global Instance embed_lequiv_m :
Proper (lequiv ==> lequiv) embed.
Global Instance lembedimpl_lentails_m:
Proper (lentails --> lentails ++> lentails) lembedimpl.
Global Instance lembedimpl_lequiv_m:
Proper (lequiv ==> lequiv ==> lequiv) lembedimpl.
Global Instance lembedand_lentails_m:
Proper (lentails ==> lentails ==> lentails) lembedand.
Global Instance lembedand_lequiv_m:
Proper (lequiv ==> lequiv ==> lequiv) lembedand.

Lemma limpllandC (P Q R : B) : P //\\ (Q -->> R) |-- Q -->> P //\\ R.