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Notation "[ rel _ _ | _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
Notation "[ rel _ _ : _ | _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
Notation "[ rel _ _ in _ & _ | _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
Notation "[ rel _ _ in _ & _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
Notation "[ rel _ _ in _ | _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
Notation "[ rel _ _ in _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
Notation "_ + _" was already used in scope nat_scope. [notation-overridden,parsing]
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Notation "[ rel _ _ | _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
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Notation "[ rel _ _ in _ & _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
Notation "[ rel _ _ in _ | _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
Notation "[ rel _ _ in _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
Notation "[ rel _ _ | _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
Notation "[ rel _ _ : _ | _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
Notation "[ rel _ _ in _ & _ | _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
Notation "[ rel _ _ in _ & _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
Notation "[ rel _ _ in _ | _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
Notation "[ rel _ _ in _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
Notation "[ rel _ _ | _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
Notation "[ rel _ _ : _ | _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
Notation "[ rel _ _ in _ & _ | _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
Notation "[ rel _ _ in _ & _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
Notation "[ rel _ _ in _ | _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
Notation "[ rel _ _ in _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
Notation "[ rel _ _ | _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
Notation "[ rel _ _ : _ | _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
Notation "[ rel _ _ in _ & _ | _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
Notation "[ rel _ _ in _ & _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
Notation "[ rel _ _ in _ | _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
Notation "[ rel _ _ in _ ]" was already used in scope fun_scope. [notation-overridden,parsing]
(** In this module, we state some general results about the [task_cost] parameter. *) Section TaskCost. (** Consider tasks and jobs with the following associated parameters. *) Context `{Task : TaskType} `{Job : JobType} `{JobTask Job Task} `{JobCost Job} `{TaskCost Task}. (** Consider a task [tsk] and a job of the task [j]. *) Variable tsk : Task. Variable j : Job. Hypothesis H_job_of_task : job_of_task tsk j. (** Assume [j] has a positive and valid cost. *) Hypothesis H_job_cost_positive : job_cost_positive j. Hypothesis H_valid_job_cost : valid_job_cost j. (** Then, the task cost of [tsk] is also positive. *)
Task: TaskType
Job: JobType
H: JobTask Job Task
H0: JobCost Job
H1: TaskCost Task
tsk: Task
j: Job
H_job_of_task: job_of_task tsk j
H_job_cost_positive: job_cost_positive j
H_valid_job_cost: valid_job_cost j

0 < task_cost tsk
Task: TaskType
Job: JobType
H: JobTask Job Task
H0: JobCost Job
H1: TaskCost Task
tsk: Task
j: Job
H_job_of_task: job_of_task tsk j
H_job_cost_positive: job_cost_positive j
H_valid_job_cost: valid_job_cost j

0 < task_cost tsk
Task: TaskType
Job: JobType
H: JobTask Job Task
H0: JobCost Job
H1: TaskCost Task
tsk: Task
j: Job
H_job_of_task: job_of_task tsk j
H_job_cost_positive: job_cost_positive j
H_valid_job_cost: valid_job_cost j

job_cost j <= task_cost tsk
by move : H_job_of_task => /eqP TSK; rewrite -TSK. Qed. End TaskCost. (** We add the above lemma to the global hints database. *) Global Hint Resolve job_cost_positive_implies_task_cost_positive: basic_rt_facts.