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By default Coq stdlib warnings raise an error, so this is really required.
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- Added derivative for asin and acos
- Added a few additional trigonometry lemmas
- Added Lemmas for the derivative of a decreasing inverse function
- Did some cleanup (move lemmas to the files where they belong)
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- minus: lemmas `Rminus_eq_0` and `Rmult_minus_distr_r`
- sin : sin_inj
- cos : cos_inj
- sqrt : lemmas `pow2_sqrt` and `inv_sqrt`
- atan : lemmas `tan_inj`, `atan_eq0`, `atan_tan` and `tan_atan`
- asin : definition and some basic properties
- acos : definition and some basic properties
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Add headers to a few files which were missing them.
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PR #9725 fixes completness bugs introduces some inefficiency. The
current PR intends to fix the inefficiency while retaining
completness. The fix removes a pre-processing step and instead relies
on a more elaborate proof format introducing positivity constraints on
the fly.
Solve bootstrapping issues: RMicromega <-> Rbase <-> lia.
Fixes #11063 and fixes #11242 and fixes #11270
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homotopy propositions and homotopy sets. Rename local variable R in test Nsatz, to avoid a name collision with the type of real numbers.
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Cauchy reals
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Redefine classical real numbers as a quotient of those constructive real numbers.
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Previously, hints added without a specified database where implicitly
put in the "core" database, which was discouraged by the user manual
(because of the lack of modularity of this approach).
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Fix new deprecation warnings in the standard library.
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Rlt_Rpower_l and pow_INR.
Unfortunately theorems Rpower_lt and Rle_power are named inconsistently,
in spite of their similarity.
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comparisons.
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This commit does not modify the signature of the involved modules, only
the opaque proof terms.
One has to wonder how proofs can bitrot so much that several occurrences
of "replace 4 with 4" start appearing.
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There are now two field structures for R: one in RealField and one in
RIneq. The first one is used to prove that IZR is a morphism which is
needed to define the second one.
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There are two main issues. First, (-cst)%R is no longer syntactically
equal to (-(cst))%R (though they are still convertible). This breaks some
rewriting rules.
Second, the ring/field_simplify tactics did not know how to refold
real constants. This defect is no longer hidden by the pretty-printer,
which makes these tactics almost unusable on goals containing large
constants.
This commit also modifies the ring/field tactics so that real constant
reification is now constant time rather than linear.
Note that there is now a bit of code duplication between z_syntax and
r_syntax. This should be fixed once plugin interdependencies are supported.
Ideally the r_syntax plugin should just disappear by declaring IZR as a
coercion. Unfortunately the coercion mechanism is not powerful enough yet,
be it for parsing (need the ability for a scope to delegate constant
parsing to another scope) or printing (too many visible coercions left).
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That way, (IZR 5) is no longer reduced to 2 + 1 + 1 + 1 (which is not
convertible to 5) but instead to 1 + 2 * 2 (which is). Moreover, it means
that, after reduction, real constants no longer exponentially blow up.
Note that I was not able to fix the test-suite for the declarative mode,
so the missing proof terms have been admitted.
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This old compatibility hint database can be safely removed
now that coq-contribs do not depend on it anymore.
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experiments about computing PI
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in Prop of constructors of inductive types independent of these names.
Incidentally upgraded/simplified a couple of proofs, mainly in Reals.
This prepares to the next commit about using names based on H for such
hypotheses in Prop.
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latent universes. Now the universes in the type of a definition/lemma
are eagerly added to the environment so that later proofs can be checked
independently of the original (delegated) proof body.
- Fixed firstorder, ring to work correctly with universe polymorphism.
- Changed constr_of_global to raise an anomaly if side effects would be lost by
turning a polymorphic constant into a constr.
- Fix a non-termination issue in solve_evar_evar.
-
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instead of a general constr: this is the most common case and does
not loose generality (one can simply define constrs before Hint Resolving
them). Benefits:
- Natural semantics for typeclasses, not class resolution needed at
Hint Resolve time, meaning less trouble for users as well.
- Ability to [Hint Remove] any hint so declared.
- Simplifies the implementation as well.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@15930 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@15715 85f007b7-540e-0410-9357-904b9bb8a0f7
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Most of these heavyweight annotations were introduced a long time ago
by the automatic 7.x -> 8.0 translator
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@15518 85f007b7-540e-0410-9357-904b9bb8a0f7
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- For instance, refl_equal --> eq_refl
- Npos, Zpos, Zneg now admit more uniform qualified aliases
N.pos, Z.pos, Z.neg.
- A new module BinInt.Pos2Z with results about injections from
positive to Z
- A result about Z.pow pushed in the generic layer
- Zmult_le_compat_{r,l} --> Z.mul_le_mono_nonneg_{r,l}
- Using tactic Z.le_elim instead of Zle_lt_or_eq
- Some cleanup in ring, field, micromega
(use of "Equivalence", "Proper" ...)
- Some adaptions in QArith (for instance changed Qpower.Qpower_decomp)
- In ZMake and ZMake, functor parameters are now named NN and ZZ
instead of N and Z for avoiding confusions
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@15515 85f007b7-540e-0410-9357-904b9bb8a0f7
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Beware that the definition of PI changes in the process
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@15425 85f007b7-540e-0410-9357-904b9bb8a0f7
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- tauto/intuition now works uniformly on and, prod, or, sum, False,
Empty_set, unit, True (and isomorphic copies of them), iff, ->, and
on all inhabited singleton types with a no-arguments constructor
such as "eq t t" (even though the last case goes out of
propositional logic: this features is so often used that it is
difficult to come back on it).
- New dtauto and dintuition works on all inductive types with one
constructors and no real arguments (for instance, they work on
records such as "Equivalence"), in addition to -> and eq-like types.
- Moreover, both of them no longer unfold inner negations (this is a
souce of incompatibility for intuition and evaluation of the level
of incompatibility on contribs still needs to be done).
Incidentally, and amazingly, fixing bug #2680 made that constants
InfA_compat and InfA_eqA in SetoidList.v lost one argument: old tauto
had indeed destructed a section hypothesis "@StrictOrder A ltA@
thinking it was a conjunction, making this section hypothesis
artificially necessary while it was not.
Renouncing to the unfolding of inner negations made auto/eauto
sometimes succeeding more, sometimes succeeding less. There is by the
way a (standard) problem with not in auto/eauto: even when given as an
"unfold hint", it works only in goals, not in hypotheses, so that auto
is not able to solve something like "forall P, (forall x, ~ P x) -> P
0 -> False". Should we automatically add a lemma of type "HYPS -> A ->
False" in the hint database everytime a lemma ""HYPS -> ~A" is
declared (and "unfold not" is a hint), and similarly for all unfold
hints?
At this occasion, also re-did some proofs of Znumtheory.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@15180 85f007b7-540e-0410-9357-904b9bb8a0f7
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It relies on Z.pos_sub instead of a Pos.compare followed by Pos.sub.
Proofs seem to be quite easy to adapt, via some rewrite Z.pos_sub_spec.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14107 85f007b7-540e-0410-9357-904b9bb8a0f7
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Initial plan was only to add shiftl/shiftr/land/... to N and
other number type, this is only partly done, but this work has
diverged into a big reorganisation and improvement session
of PArith,NArith,ZArith.
Bool/Bool: add lemmas orb_diag (a||a = a) and andb_diag (a&&a = a)
PArith/BinPos:
- added a power function Ppow
- iterator iter_pos moved from Zmisc to here + some lemmas
- added Psize_pos, which is 1+log2, used to define Nlog2/Zlog2
- more lemmas on Pcompare and succ/+/* and order, allow
to simplify a lot some old proofs elsewhere.
- new/revised results on Pminus (including some direct proof of
stuff from Pnat)
PArith/Pnat:
- more direct proofs (limit the need of stuff about Pmult_nat).
- provide nicer names for some lemmas (eg. Pplus_plus instead of
nat_of_P_plus_morphism), compatibility notations provided.
- kill some too-specific lemmas unused in stdlib + contribs
NArith/BinNat:
- N_of_nat, nat_of_N moved from Nnat to here.
- a lemma relating Npred and Nminus
- revised definitions and specification proofs of Npow and Nlog2
NArith/Nnat:
- shorter proofs.
- stuff about Z_of_N is moved to Znat. This way, NArith is
entirely independent from ZArith.
NArith/Ndigits:
- added bitwise operations Nand Nor Ndiff Nshiftl Nshiftr
- revised proofs about Nxor, still using functional bit stream
- use the same approach to prove properties of Nand Nor Ndiff
ZArith/BinInt: huge simplification of Zplus_assoc + cosmetic stuff
ZArith/Zcompare: nicer proofs of ugly things like Zcompare_Zplus_compat
ZArith/Znat: some nicer proofs and names, received stuff about Z_of_N
ZArith/Zmisc: almost empty new, only contain stuff about badly-named
iter. Should be reformed more someday.
ZArith/Zlog_def: Zlog2 is now based on Psize_pos, this factorizes
proofs and avoid slowdown due to adding 1 in Z instead of in positive
Zarith/Zpow_def: Zpower_opt is renamed more modestly Zpower_alt
as long as I dont't know why it's slower on powers of two.
Elsewhere: propagate new names + some nicer proofs
NB: Impact on compatibility is probably non-zero, but should be
really moderate. We'll see on contribs, but a few Require here
and there might be necessary.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13651 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13323 85f007b7-540e-0410-9357-904b9bb8a0f7
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- Many of them were broken, some of them after Pierre B's rework
of mli for ocamldoc, but not only (many bad annotation, many files
with no svn property about Id, etc)
- Useless for those of us that work with git-svn (and a fortiori
in a forthcoming git-only setting)
- Even in svn, they seem to be of little interest
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12972 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12380 85f007b7-540e-0410-9357-904b9bb8a0f7
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