Section AlwaysInductiveInv.
Variable pr : protocol.
(* Decompose the initial protocol *)
Notation l := (plab pr).
Notation coh := (coh pr).
Variable I : dstatelet -> pred nid -> Prop.
Variable ii : InductiveInv pr I.
(* Tailored modal always-lemma *)
Variables (A : Type) (this: nid).
Notation V := (mkWorld pr).
Notation W := (mkWorld (ProtocolWithIndInv ii)).

Lemma aft_ind_inv (p : proc this V A) (P : A -> state -> Prop) i :
i \In Coh W ->
after i p P ->
after i (WithInv pr I ii (erefl _) p)
(fun v m => m \In Coh W /\ P v m).