The two new lemmas allow splitting the resources in one component
of a pair when the other component has nothing. In combination
with `pair_split`, they allow to arbitrarily split the resource
`(a ⋅ a', b ⋅ b')`.

This is in line with `prod_local_update_1` and
`prod_local_update_2`, the lemmas that allow, in a sense, to only
consider one component of a pair.

To prepare for https://github.com/coq/coq/pull/10762

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 (??).

Simon knows why ;)

Turn all `f_op` lemmas to have shape `f (x ⋅ y) = f x ⋅ f y`, following the plan
in iris/iris!295 (comment 39151), plus
`cmra_morphism_op`.

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")

This allows one to make use of recursive ghost state obtained from the
recursive domain equation solver.

We never make canonical instances of them.

This comment wasn't updated after
866cad62.

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).

Thanks to @jung for proposing these names.

The finiteness was needed to have the axiom of choice over the domain. This axiom is not needed if cmra_extend is in Type.

Revert "Remove the domain finiteness hypothesis for the function CMRA, and put cmra_extend in Type."

This reverts commit fa897ff5.

The finiteness was needed to have the axiom of choice over the domain. This axiom is not needed if cmra_extend is in Type.

In same spirit as the other 'primitive' types like `option`, `prod`, ...