| Commit message (Collapse) | Author | Age |
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See now https://github.com/coq/bignums
Int31 is still in the stdlib.
Some proofs there has be adapted to avoid the need for BigNumPrelude.
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~True.
Found 1 incompatibility in tested contribs and 3 times the same
pattern of incompatibility in the standard library. In all cases, it
is an improvement in the form of the script.
New behavior deactivated when version is <= 8.5.
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There were three versions of injection:
1. "injection term" without "as" clause:
was leaving hypotheses on the goal in reverse order
2. "injection term as ipat", first version:
was introduction hypotheses using ipat in reverse order without
checking that the number of ipat was the size of the injection
(activated with "Unset Injection L2R Pattern Order")
3. "injection term as ipat", second version:
was introduction hypotheses using ipat in left-to-right order
checking that the number of ipat was the size of the injection
and clearing the injecting term by default if an hypothesis
(activated with "Set Injection L2R Pattern Order", default one from 8.5)
There is now:
4. "injection term" without "as" clause, new version:
introducing the components of the injection in the context in
left-to-right order using default intro-patterns "?"
and clearing the injecting term by default if an hypothesis
(activated with "Set Structural Injection")
The new versions 3. and 4. are the "expected" ones in the sense that
they have the following good properties:
- introduction in the context is in the natural left-to-right order
- "injection" behaves the same with and without "as", always
introducing the hypotheses in the goal what corresponds to the
natural expectation as the changes I made in the proof scripts for
adaptation confirm
- clear the "injection" hypothesis when an hypothesis which is the
natural expectation as the changes I made in the proof scripts for
adaptation confirm
The compatibility can be preserved by "Unset Structural Injection" or
by calling "simple injection".
The flag is currently off.
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- The earlier proof-of-concept file NPeano (which instantiates
the "Numbers" framework for nat) becomes now the entry point
in the Arith lib, and gets renamed PeanoNat. It still provides
an inner module "Nat" which sums up everything about type nat
(functions, predicates and properties of them).
This inner module Nat is usable as soon as you Require Import Arith,
or just Arith_base, or simply PeanoNat.
- Definitions of operations over type nat are now grouped in a new
file Init/Nat.v. This file is meant to be used without "Import",
hence providing for instance Nat.add or Nat.sqrt as soon as coqtop
starts (but no proofs about them).
- The definitions that used to be in Init/Peano.v (pred, plus, minus, mult)
are now compatibility notations (for Nat.pred, Nat.add, Nat.sub, Nat.mul
where here Nat is Init/Nat.v).
- This Coq.Init.Nat module (with only pure definitions) is Include'd
in the aforementioned Coq.Arith.PeanoNat.Nat. You might see Init.Nat
sometimes instead of just Nat (for instance when doing "Print plus").
Normally it should be ok to just ignore these "Init" since
Init.Nat is included in the full PeanoNat.Nat. I'm investigating if
it's possible to get rid of these "Init" prefixes.
- Concerning predicates, orders le and lt are still defined in Init/Peano.v,
with their notations "<=" and "<". Properties in PeanoNat.Nat directly
refer to these predicates in Peano. For instantation reasons, PeanoNat.Nat
also contains a Nat.le and Nat.lt (defined via "Definition le := Peano.le",
we cannot yet include an Inductive to implement a Parameter), but these
aliased predicates won't probably be very convenient to use.
- Technical remark: I've split the previous property functor NProp in
two parts (NBasicProp and NExtraProp), it helps a lot for building
PeanoNat.Nat incrementally. Roughly speaking, we have the following schema:
Module Nat.
Include Coq.Init.Nat. (* definition of operations : add ... sqrt ... *)
... (** proofs of specifications for basic ops such as + * - *)
Include NBasicProp. (** generic properties of these basic ops *)
... (** proofs of specifications for advanced ops (pow sqrt log2...)
that may rely on proofs for + * - *)
Include NExtraProp. (** all remaining properties *)
End Nat.
- All other files in directory Arith are now taking advantage of PeanoNat :
they are now filled with compatibility notations (when earlier lemmas
have exact counterpart in the Nat module) or lemmas with one-line proofs
based on the Nat module. All hints for database "arith" remain declared
in these old-style file (such as Plus.v, Lt.v, etc). All the old-style
files are still Require'd (or not) by Arith.v, just as before.
- Compatibility should be almost complete. For instance in the stdlib,
the only adaptations were due to .ml code referring to some Coq constant
name such as Coq.Init.Peano.pred, which doesn't live well with the
new compatibility notations.
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When arguments scopes are set manually, nothing new, they stay
as they are (until maybe another Arguments invocation).
But when argument scopes are computed out of the argument type and
the Bind Scope information, this kind of scope is now dynamic:
a later Bind Scope will be able to impact the scopes of an earlier
constant. For Instance:
Definition f (n:nat) := n.
About f. (* Argument scope is [nat_scope] *)
Bind Scope other_scope with nat.
About f. (* Argument scope is [other_scope] *)
This allows to get rid of hacks for modifying scopes during functor
applications. Moreover, the subst_arguments_scope is now
environment-insensitive (needed for forthcoming changes in declaremods).
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@16626 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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The ugly syntax "destruct x as [ ]_eqn:H" is replaced by:
destruct x eqn:H
destruct x as [ ] eqn:H
Some with induction. Of course, the pattern behind "as" is arbitrary.
For an anonymous version, H could be replaced by ?. The old syntax
with "_eqn" still works for the moment, by triggers a warning.
For making this new syntax work, we had to change the seldom-used
"induction x y z using foo" into "induction x, y, z using foo".
Now, only one "using" can be used per command instead of one per
comma-separated group earlier, but I doubt this will bother anyone.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@15566 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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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14718 85f007b7-540e-0410-9357-904b9bb8a0f7
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This adds two experimental features to the typeclass implementation:
- Path cuts: a way to specify through regular expressions on instance names
search pathes that should be avoided (e.g. [proper_flip proper_flip]).
Regular expression matching is implemented through naïve derivatives.
- Forward hints for subclasses: e.g. [Equivalence -> Reflexive] is no
longer applied backwards, but introducing a specific [Equivalence] in the
environment register a [Reflexive] hint as well. Currently not
backwards-compatible, the next patch will allow to specify direction
of subclasses hints.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14671 85f007b7-540e-0410-9357-904b9bb8a0f7
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Instead of hard-coding in search.ml some substrings such
as "_admitted" or "_subproof" we don't want to see in results
of SearchAbout and co, we now have a user command:
Add Search Blacklist "foo".
Remove Search Blacklist "foo". (* the opposite *)
Print Table Search Blacklist. (* the current state *)
In Prelude.v, three substrings are blacklisted originally:
- "_admitted" for internal lemmas due to admit.
- "_subproof" for internal lemmas due to abstract.
- "Private_" for hiding auxiliary modules not meant for
global usage.
Note that substrings are searched in the fully qualified names
of the available lemmas (e.g. "Coq.Init.Peano.plus").
This commit also adds the prefix "Private_" to some internal modules
in Numbers, Z, N, etc.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14408 85f007b7-540e-0410-9357-904b9bb8a0f7
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- Zpow_def, Zpower, Zpow_facts shortened thanks to stuff in BinInt.Z
- The alternative Zpower_alt is now in a separate file Zpow_alt.v,
not loaded by default.
- Some more injection lemmas in Znat (pow, div, mod, quot, rem)
- Btw, added a "square" function in Z, N, Pos, ... (instead of
Zpow_facts.Zsquare).
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14253 85f007b7-540e-0410-9357-904b9bb8a0f7
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Note that in NSig (and hence NMake and BigN), to_N is now
Z.to_N (to_Z ...) instead of Z.abs_N (to_Z ...). This doesn't
change the result (since to_Z create non-negative integers),
but some proofs may have to be adapted
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14250 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14247 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14246 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14245 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14244 85f007b7-540e-0410-9357-904b9bb8a0f7
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In particular, we merge the old Zdivide (used to be an ad-hoc
inductive predicate) and the new Z.divide (based on exists).
Notations allow to do that (almost) transparently, the only
impact is that the name picked by the system will not be "q"
anymore when destructing a Z.divide. Some fragile scripts
may have to be fixed.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14239 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14238 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14237 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14230 85f007b7-540e-0410-9357-904b9bb8a0f7
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Start of a uniform treatment of compare, eqb, leb, ltb:
- We now ensure that they are provided by N,Z,BigZ,BigN,Nat and Pos
- Some generic properties are derived in OrdersFacts.BoolOrderFacts
In BinPos, more work about sub_mask with nice implications
on compare (e.g. simplier proof of lt_trans).
In BinNat/BinPos, for uniformity, compare_antisym is now
(y ?= x) = CompOpp (x ?=y) instead of the symmetrical result.
In BigN / BigZ, eq_bool is now eqb
In BinIntDef, gtb and geb are kept for the moment, but
a comment advise to rather use ltb and leb. Z.div now uses
Z.ltb and Z.leb.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14227 85f007b7-540e-0410-9357-904b9bb8a0f7
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All the functions about Z is now in a separated file BinIntDef,
which is Included in BinInt.Z. This BinInt.Z directly
implements ZAxiomsSig, and instantiates derived properties ZProp.
Note that we refer to Z instead of t inside BinInt.Z,
otherwise ring breaks later on @eq Z.t
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14106 85f007b7-540e-0410-9357-904b9bb8a0f7
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CompareSpec expects 3 propositions Peq Plt Pgt instead of 2 relations
eq lt and 2 points x y. For the moment, we still always use (Peq=eq x y),
(Plt=lt x y) (Pgt=lt y x), but this may not be always the case,
especially for Pgt. The former CompSpec is now defined in term of
CompareSpec. Compatibility is preserved (except maybe a rare unfold
or red to break the CompSpec definition).
Typically, CompareSpec looks nicer when we have infix notations, e.g.
forall x y, CompareSpec (x=y) (x<y) (y<x) (x?=x)
while CompSpec is shorter when we directly refer to predicates:
forall x y, CompSpec eq lt x y (compare x y)
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13914 85f007b7-540e-0410-9357-904b9bb8a0f7
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Initial patch by Robbert Krebbers.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13900 85f007b7-540e-0410-9357-904b9bb8a0f7
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For Argument Scope, we now record types (more precisely classes cl_typ)
in addition to scope list. After substitution (e.g. at functor application),
the new types are used to search for corresponding concrete scopes.
Currently, this automatic scope substitution of argument scope takes
precedence (if successful) over scope declared in the functor (even
by the user). On the opposite, the manual scope substitution
(cf last commit introducing annotation [scope foo to bar])
is done _after_ the automatic scope substitution.
TODO: if this behavior is satisfactory, document it ...
Note that Classops.find_class_type lose its env args since it was
actually unused, and is now used for Notation.find_class
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13840 85f007b7-540e-0410-9357-904b9bb8a0f7
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- The experimental syntax "<30>F M" is transformed into "F M [inline at level 30]"
- The earlier syntax !F X should now be written "F X [no inline]"
(note that using ! is still possible for compatibility)
- A new annotation "F M [scope foo_scope to bar_scope]" allow to substitute
foo_scope by bar_scope in all arguments scope of objects in F.
BigN and BigZ are cleaned from the zillions of Arguments Scope used earlier.
Arguments scope for lemmas are fixed for instances of Numbers.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13839 85f007b7-540e-0410-9357-904b9bb8a0f7
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We now specify testbit by some initial and recursive equations.
The previous spec (via a complex split of the number in
low and high parts) is now a derived property in {N,Z}Bits.v
This way, proofs of implementations are quite simplier.
Note that these new specs doesn't imply anymore that testbit is a
morphism, we have to add this as a extra spec (but this lead
to trivial proofs when implementing).
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13792 85f007b7-540e-0410-9357-904b9bb8a0f7
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For example, if we know that [f] is a morphism for [E1==>E2==>E],
then the goal [E (f x y) (f x' y')] will be transformed by [f_equiv]
into the subgoals [E1 x x'] and [E2 y y'].
This way, we can remove most of the explicit use of the morphism
instances in Numbers (lemmas foo_wd for each operator foo).
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13763 85f007b7-540e-0410-9357-904b9bb8a0f7
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- a ltac solve_proper which generalizes solve_predicate_wd and co
- using le_elim is nicer that (apply le_lteq; destruct ...)
- "apply ->" can now be "apply" most of the time.
Benefit: NumPrelude is now almost empty
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13762 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13721 85f007b7-540e-0410-9357-904b9bb8a0f7
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To avoid names¬ations clashs with list, Vector shouldn't be
"Import"ed but one can "Import Vector.VectorNotations." to have
notations.
SetoidVector at least remains to do.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13702 85f007b7-540e-0410-9357-904b9bb8a0f7
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Now we have:
- Zdiv and Zdiv2 : round toward bottom, no easy sign rule, remainder
of a/2 is 0 or 1, operations related with two's-complement Zshiftr.
- Zquot and Zquot2 : round toward zero, Zquot2 (-a) = - Zquot2 a,
remainder of a/2 is 0 or Zsgn a.
Ok, I'm introducing an incompatibility here, but I think coherence is
really desirable. Anyway, people using Zdiv on positive numbers only
shouldn't even notice the change. Otherwise, it's just a matter of
sed -e "s/div2/quot2/g".
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13695 85f007b7-540e-0410-9357-904b9bb8a0f7
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See NatInt/NZBits.v for the common axiomatization of bitwise functions
over naturals / integers. Some specs aren't pretty, but easier to
prove, see alternate statements in property functors {N,Z}Bits.
Negative numbers are considered via the two's complement convention.
We provide implementations for N (in Ndigits.v), for nat (quite dummy,
just for completeness), for Z (new file Zdigits_def), for BigN
(for the moment partly by converting to N, to be improved soon)
and for BigZ.
NOTA: For BigN.shiftl and BigN.shiftr, the two arguments are now in
the reversed order (for consistency with the rest of the world):
for instance BigN.shiftl 1 10 is 2^10.
NOTA2: Zeven.Zdiv2 is _not_ doing (Zdiv _ 2), but rather (Zquot _ 2)
on negative numbers. For the moment I've kept it intact, and have
just added a Zdiv2' which is truly equivalent to (Zdiv _ 2).
To reorganize someday ?
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13689 85f007b7-540e-0410-9357-904b9bb8a0f7
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Some more results about sqrt. Similar results for sqrt_up.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13649 85f007b7-540e-0410-9357-904b9bb8a0f7
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as log2
Some more results about log2. Similar results for log2_up.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13648 85f007b7-540e-0410-9357-904b9bb8a0f7
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No infix notation "rem" for Zrem (that will probably become Z.rem in
a close future). This way, we avoid conflict with people already using
rem for their own need. Same for BigZ. We still use infix rem, but
only in the abstract layer of Numbers, in a way that doesn't inpact
the rest of Coq. Btw, the axiomatized function is now named rem
instead of remainder.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13640 85f007b7-540e-0410-9357-904b9bb8a0f7
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(floor convention).
We follow Haskell naming convention: quot and rem are for
Round-Toward-Zero (a.k.a Trunc, what Ocaml, C, Asm do by default, cf.
the ex-ZOdiv file), while div and mod are for Round-Toward-Bottom
(a.k.a Floor, what Coq does historically in Zdiv). We use unicode ÷
for quot, and infix rem for rem (which is actually remainder in
full). This way, both conventions can be used at the same time.
Definitions (and proofs of specifications) for div mod quot rem are
migrated in a new file Zdiv_def. Ex-ZOdiv file is now Zquot. With
this new organisation, no need for functor application in Zdiv and
Zquot.
On the abstract side, ZAxiomsSig now provides div mod quot rem.
Zproperties now contains properties of them. In NZDiv, we stop
splitting specifications in Common vs. Specific parts. Instead,
the NZ specification is be extended later, even if this leads to
a useless mod_bound_pos, subsumed by more precise axioms.
A few results in ZDivTrunc and ZDivFloor are improved (sgn stuff).
A few proofs in Nnat, Znat, Zabs are reworked (no more dependency
to Zmin, Zmax).
A lcm (least common multiple) is derived abstractly from gcd and
division (and hence available for nat N BigN Z BigZ :-).
In these new files NLcm and ZLcm, we also provide some combined
properties of div mod quot rem gcd.
We also provide a new file Zeuclid implementing a third division
convention, where the remainder is always positive. This file
instanciate the abstract one ZDivEucl. Operation names are
ZEuclid.div and ZEuclid.modulo.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13633 85f007b7-540e-0410-9357-904b9bb8a0f7
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- For nat, we create a brand-new gcd function, structural in
the sense of Coq, even if it's Euclid algorithm. Cool...
- We re-organize the Zgcd that was in Znumtheory, create out of it
files Pgcd, Ngcd_def, Zgcd_def. Proofs of correctness are revised
in order to be much simpler (no omega, no advanced lemmas of
Znumtheory, etc).
- Abstract Properties NZGcd / ZGcd / NGcd could still be completed,
for the moment they contain up to Gauss thm. We could add stuff
about (relative) primality, relationship between gcd and div,mod,
or stuff about parity, etc etc.
- Znumtheory remains as it was, apart for Zgcd and correctness proofs
gone elsewhere. We could later take advantage of ZGcd in it.
Someday, we'll have to switch from the current Zdivide inductive,
to Zdivide' via exists. To be continued...
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13623 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13609 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13608 85f007b7-540e-0410-9357-904b9bb8a0f7
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Théo Zimmermann
Maxime Dénès
Pierre-Marie Pédrot
Russell O'Connor
Pierre Letouzey
Hugo Herbelin
Guillaume Melquiond
letouzey
herbelin
gareuselesinge
msozeau
pboutill