Set Implicit Arguments.
Unset Strict Implicit.
Set Maximal Implicit Insertion.
Local Existing Instance ILPre_Ops.
Local Existing Instance ILPre_ILogic.
Local Existing Instance ILFun_Ops.
Local Existing Instance ILFun_ILogic.
(*Local Existing Instance EquivPreorder.*)
Local Transparent ILPre_Ops.
Local Transparent ILFun_Ops.
Local Transparent BILPre_Ops.
Local Transparent BILFun_Ops.
Local Transparent ILLaterPreOps.
Local Transparent ILLaterNatOps.
Section ILogic_Pre.
Context T (ord: relation T) {HPre : PreOrder ord}.
Context {A : Type} `{IL: ILogic A}.

Lemma ILPreFrm_apply {P Q : ILPreFrm ord _} (x : T) (H : P |-- Q) : P x |-- Q x.
End ILogic_Pre.