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Co-authored-by: Cyril Cohen <CohenCyril@users.noreply.github.com>
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This change reduces
- use of numerical occurrence selectors (#436) and
- use of non ssreflect tactics such as `auto`,
and improves use of comparison predicates such as `posnP`, `leqP`, `ltnP`,
`ltngtP`, and `eqVneq`.
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needed lemmas (#261)
* adds relevant theorems when fcycle f (orbit f x) and the needed lemmas
* Generalize f_step lemmas
* Generalizations, shorter proofs, bugfixes, CHANGELOG
- changelog, renamings and comments
- renaming `homo_cycle` to `mem_fcycle` and other small renamings
- name swap `mem_orbit` and `in_orbit`
- simplifications
- generalization following @pi8027's comment
- Getting rid of many uniquness condition in `fingraph.v`
- added cases to the equivalence `orbitPcycle`
- added `cycle_catC`
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Use `{pred T}` systematically for generic _collective_ boolean
predicate.
Use `PredType` to construct `predType` instances.
Instrument core `ssreflect` files to replicate these and other new
features introduces by coq/coq#9555 (`nonPropType` interface,
`simpl_rel` that simplifies with `inE`).
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while some refs (see e.g. [1]) don't assume that the "transitive closure" is
reflexive; so one won't need to look at lemma "connect0" to figure this out.
[1] https://en.wikipedia.org/wiki/Transitive_closure
[ci skip]
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```
Warning: Adding and removing hints in the core database implicitly is
deprecated. Please specify a hint database.
[implicit-core-hint-db,deprecated]
```
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See the discussion here:
https://github.com/math-comp/math-comp/pull/242#discussion_r233778114
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- f_finv
- finv_f
- fconnect_sym
- iter_order
- iter_finv
- cycle_orbit
- fpath_finv (* I need to sub-theorems for this case. *)
All generalizations are named "..._in" the existing theorems are now
instances of the generalizations.
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