Paolo G. Giarrusso authored 5 years ago and Robbert Krebbers committed 5 years ago

When proving `foo` through a fixpoint, Coq's guardedness checker needs to see to
which arguments `foo` is applied. Opaque lemmas applied to `foo` itself prevent
that, so make them transparent.
* Make `IntoEmpValid` lemmas transparent.
* Expose application of `IntoEmpValid` instance to its argument.
* Add comment to `tac_pose_proof`

This MR brings back the type of `tac_pose_proof` to the one it had before !329.
Hence, this seems worth a comment.

This test case arose in Iron.

Also, rewrite `iIntoEmpValid`. Now, instead of using Ltac to traverse
the type of the term and generate goals for the premises, we repeatedly
apply a series of lemmas. This has the advantage that it works up to
convertability, and we no longer need the `eval ...` hacks.

Fix issue pointed out by @tchajed in iris/iris!330 (comment 41322)

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 (??).

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`.

This also gets rid of [val_for_compare]-normalization; instead we introduce a
[LitErased] literal that is suited for use by erasure theorems.

This is the name used by x86 (CMPXCHG) and LLVM.  Also reorder the result (value
first, boolean second) for consistency with LLVM, because why not.

This avoids weird Ltac behaviors like those in !272.

Also, change `before_tc` keyword into `as` to be consistent with other tactics.

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")