The general idea is to first import/export modules which are further
than the current one, and then import/export modules which are close
dependencies.

This commit tries to use the same order of imports for every file, and
describes the convention in ProofGuide.md. There is one exception,
where we do not follow said convention: in program_logic/weakestpre.v,
using that order would break printing of texan triples (??).

- And use prop_ext instead of prop_ext_2 in other proofs.

Dan Frumin authored 5 years ago and Robbert Krebbers committed 5 years ago

And shorten the proof.

Used the following script:

sed '
s/\bCofeMor/OfeMor/g;
s/\-c>/\-d>/g;
s/\bcFunctor/oFunctor/g;
s/\bCFunctor/OFunctor/g;
s/\b\%CF/\%OF/g;
s/\bconstCF/constOF/g;
s/\bidCF/idOF/g
s/\bdiscreteC/discreteO/g;
s/\bleibnizC/leibnizO/g;
s/\bunitC/unitO/g;
s/\bprodC/prodO/g;
s/\bsumC/sumO/g;
s/\bboolC/boolO/g;
s/\bnatC/natO/g;
s/\bpositiveC/positiveO/g;
s/\bNC/NO/g;
s/\bZC/ZO/g;
s/\boptionC/optionO/g;
s/\blaterC/laterO/g;
s/\bofe\_fun/discrete\_fun/g;
s/\bdiscrete\_funC/discrete\_funO/g;
s/\bofe\_morC/ofe\_morO/g;
s/\bsigC/sigO/g;
s/\buPredC/uPredO/g;
s/\bcsumC/csumO/g;
s/\bagreeC/agreeO/g;
s/\bauthC/authO/g;
s/\bnamespace_mapC/namespace\_mapO/g;
s/\bcmra\_ofeC/cmra\_ofeO/g;
s/\bucmra\_ofeC/ucmra\_ofeO/g;
s/\bexclC/exclO/g;
s/\bgmapC/gmapO/g;
s/\blistC/listO/g;
s/\bvecC/vecO/g;
s/\bgsetC/gsetO/g;
s/\bgset\_disjC/gset\_disjO/g;
s/\bcoPsetC/coPsetO/g;
s/\bgmultisetC/gmultisetO/g;
s/\bufracC/ufracO/g
s/\bfracC/fracO/g;
s/\bvalidityC/validityO/g;
s/\bbi\_ofeC/bi\_ofeO/g;
s/\bsbi\_ofeC/sbi\_ofeO/g;
s/\bmonPredC/monPredO/g;
s/\bstateC/stateO/g;
s/\bvalC/valO/g;
s/\bexprC/exprO/g;
s/\blocC/locO/g;
' -i $(find theories -name "*.v")

Notably, `big_andL_andL` and `big_andL_and` where a ⊣⊢ and ⊢ version
of the same lemma. I favored the `big_opL_op` naming scheme.

The `2: { ... }` syntax is not yet supported there.

This is in preparation for coq/coq#9274.

Adding a hint without a database now triggers a deprecation warning in
Coq master (https://github.com/coq/coq/pull/8987).