Points before or after an interval are not in the interval...

n + a - b + b - a = n if n >= b

...to match leq_ltn_trans in ssrnat

To allow reasoning about an entire class of types of schedules /
processor modules, it's useful to have named definitions for various
invariants that processor models ensure. Let's collect these centrally
where we introduce processor models and schedules.

Maxime Lesourd authored 5 years ago and Björn Brandenburg committed 5 years ago

Add model definitions for work-conserving and priority-based preemptive schedules.

Maxime Lesourd authored 5 years ago and Björn Brandenburg committed 5 years ago

This is a port (+additions) of the definitions and semantics for arrival curves (model/arrival/curves.v). As a prerequisite, this includes definitions about activations of a task (model/task_arrivals.v).

Two additional definitions which were not found in the original library but will be useful to us in the future:

* in schedule.v : completes_at
* in task_arrivals.v : arrivals_come_from_taskset

simplify structure of behavior, move arrival_sequence and schedule to toplevel, move task and sequential to model

- Consistently use JobType rather than eqType directly.
- Fix the comments style.

Coqdoc produces really nice output - let's automate this.

There's no need to run this for every compiler version; we only care
about the "main" version.

This avoids having to compile ssreflect from scratch each time we want
to compile Prosa.

Thanks to Pierre Roux (Pierre.Roux@onera.fr) for pointing out the
mathcomp Docker images!

From the mathcomp 1.9.0 release notes:

> removed Coq prelude hints plus_n_O plus_n_Sm mult_n_O mult_n_Sm, to
> improve robustness of by ...; scripts may need to invoke addn0,
> addnS, muln0 or mulnS explicitly where these hints were used
> accidentally.

=> This patch makes these required fixes in Prosa.

While at it, turn on CI for coq:dev and Coq 8.9 with two versions of ssreflect.

Using the official Coq Docker images kindly provided by the Coq community:

	https://github.com/coq-community/docker-coq/wiki/CI-setup

Using the following CI template as a starting point:

	https://gitlab.com/erikmd/docker-coq-gitlab-ci-demo-1/blob/master/.gitlab-ci.yml

...and introduce a bunch of helper lemmas to get there.