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# Library prosa.analysis.definitions.carry_in

Require Export prosa.model.priority.classes.

# No Carry-In

In this module, we define the notion of a time without any carry-in work.
Section NoCarryIn.
Consider any type of tasks ...
Context {Task : TaskType}.
Context `{TaskCost Task}.
... and any type of jobs associated with these tasks, where each job has an arrival time and a cost.
Context {Job : JobType} `{JobTask Job Task} `{JobArrival Job} `{JobCost Job}.
Consider any arrival sequence of such jobs with consistent arrivals ...
Variable arr_seq : arrival_sequence Job.
Hypothesis H_arrival_times_are_consistent : consistent_arrival_times arr_seq.
... and the resultant schedule.
Context {PState : ProcessorState Job}.
Variable sched : schedule PState.
There is no carry-in at time t iff every job (regardless of priority) from the arrival sequence released before t has completed by that time.
Definition no_carry_in (t : instant) :=
∀ j_o,
arrives_in arr_seq j_o →
arrived_before j_o t →
completed_by sched j_o t.
End NoCarryIn.