Moving never-used comments from Zhints.v to dev/doc so as not to

obfuscate the standard library.

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14505 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 0 insertions, 437 deletions

diff --git a/theories/ZArith/Zhints.v b/theories/ZArith/Zhints.v
index 731f0252f..6a14d6934 100644
--- a/theories/ZArith/Zhints.v
+++ b/theories/ZArith/Zhints.v
@@ -98,440 +98,3 @@ Hint Resolve
   Zplus_le_compat (* :(n,m,p,q:Z)`n <= m`->`p <= q`->`n+p <= m+q` *)
 
   : zarith.
-
-(**********************************************************************)
-(** *        Reversible lemmas relating operators                     *)
-(** Probably to be declared as hints but need to define precedences   *)
-
-(** ** Conversion between comparisons/predicates and arithmetic operators *)
-
-(** Lemmas ending by eq *)
-(**
-<<
-Zegal_left: (x,y:Z)`x = y`->`x+(-y) = 0`
-Zabs_eq: (x:Z)`0 <= x`->`|x| = x`
-Zeven_div2: (x:Z)(Zeven x)->`x = 2*(Zdiv2 x)`
-Zodd_div2: (x:Z)`x >= 0`->(Zodd x)->`x = 2*(Zdiv2 x)+1`
->>
-*)
-
-(** Lemmas ending by Zgt *)
-(**
-<<
-Zgt_left_rev: (x,y:Z)`x+(-y) > 0`->`x > y`
-Zgt_left_gt: (x,y:Z)`x > y`->`x+(-y) > 0`
->>
-*)
-
-(** Lemmas ending by Zlt *)
-(**
-<<
-Zlt_left_rev: (x,y:Z)`0 < y+(-x)`->`x < y`
-Zlt_left_lt: (x,y:Z)`x < y`->`0 < y+(-x)`
-Zlt_O_minus_lt: (n,m:Z)`0 < n-m`->`m < n`
->>
-*)
-
-(** Lemmas ending by Zle *)
-(**
-<<
-Zle_left: (x,y:Z)`x <= y`->`0 <= y+(-x)`
-Zle_left_rev: (x,y:Z)`0 <= y+(-x)`->`x <= y`
-Zlt_left: (x,y:Z)`x < y`->`0 <= y+(-1)+(-x)`
-Zge_left: (x,y:Z)`x >= y`->`0 <= x+(-y)`
-Zgt_left: (x,y:Z)`x > y`->`0 <= x+(-1)+(-y)`
->>
-*)
-
-(** ** Conversion between nat comparisons and Z comparisons *)
-
-(** Lemmas ending by eq *)
-(**
-<<
-inj_eq: (x,y:nat)x=y->`(inject_nat x) = (inject_nat y)`
->>
-*)
-
-(** Lemmas ending by Zge *)
-(**
-<<
-inj_ge: (x,y:nat)(ge x y)->`(inject_nat x) >= (inject_nat y)`
->>
-*)
-
-(** Lemmas ending by Zgt *)
-(**
-<<
-inj_gt: (x,y:nat)(gt x y)->`(inject_nat x) > (inject_nat y)`
->>
-*)
-
-(** Lemmas ending by Zlt *)
-(**
-<<
-inj_lt: (x,y:nat)(lt x y)->`(inject_nat x) < (inject_nat y)`
->>
-*)
-
-(** Lemmas ending by Zle *)
-(**
-<<
-inj_le: (x,y:nat)(le x y)->`(inject_nat x) <= (inject_nat y)`
->>
-*)
-
-(** ** Conversion between comparisons *)
-
-(** Lemmas ending by Zge *)
-(**
-<<
-not_Zlt: (x,y:Z)~`x < y`->`x >= y`
-Zle_ge: (m,n:Z)`m <= n`->`n >= m`
->>
-*)
-
-(** Lemmas ending by Zgt *)
-(**
-<<
-Zle_gt_S: (n,p:Z)`n <= p`->`(Zs p) > n`
-not_Zle: (x,y:Z)~`x <= y`->`x > y`
-Zlt_gt: (m,n:Z)`m < n`->`n > m`
-Zle_S_gt: (n,m:Z)`(Zs n) <= m`->`m > n`
->>
-*)
-
-(** Lemmas ending by Zlt *)
-(**
-<<
-not_Zge: (x,y:Z)~`x >= y`->`x < y`
-Zgt_lt: (m,n:Z)`m > n`->`n < m`
-Zle_lt_n_Sm: (n,m:Z)`n <= m`->`n < (Zs m)`
->>
-*)
-
-(** Lemmas ending by Zle *)
-(**
-<<
-Zlt_ZERO_pred_le_ZERO: (x:Z)`0 < x`->`0 <= (Zpred x)`
-not_Zgt: (x,y:Z)~`x > y`->`x <= y`
-Zgt_le_S: (n,p:Z)`p > n`->`(Zs n) <= p`
-Zgt_S_le: (n,p:Z)`(Zs p) > n`->`n <= p`
-Zge_le: (m,n:Z)`m >= n`->`n <= m`
-Zlt_le_S: (n,p:Z)`n < p`->`(Zs n) <= p`
-Zlt_n_Sm_le: (n,m:Z)`n < (Zs m)`->`n <= m`
-Zlt_le_weak: (n,m:Z)`n < m`->`n <= m`
-Zle_refl: (n,m:Z)`n = m`->`n <= m`
->>
-*)
-
-(** ** Irreversible simplification involving several comparaisons *)
-(**    useful with clear precedences *)
-
-(** Lemmas ending by Zlt *)
-(**
-<<
-Zlt_le_reg :(a,b,c,d:Z)`a < b`->`c <= d`->`a+c < b+d`
-Zle_lt_reg : (a,b,c,d:Z)`a <= b`->`c < d`->`a+c < b+d`
->>
-*)
-
-(** ** What is decreasing here ? *)
-
-(** Lemmas ending by eq *)
-(**
-<<
-Zplus_minus: (n,m,p:Z)`n = m+p`->`p = n-m`
->>
-*)
-
-(** Lemmas ending by Zgt *)
-(**
-<<
-Zgt_pred: (n,p:Z)`p > (Zs n)`->`(Zpred p) > n`
->>
-*)
-
-(** Lemmas ending by Zlt *)
-(**
-<<
-Zlt_pred: (n,p:Z)`(Zs n) < p`->`n < (Zpred p)`
->>
-*)
-
-(**********************************************************************)
-(** *                Useful Bottom-up lemmas                          *)
-
-(** ** Bottom-up simplification: should be used *)
-
-(** Lemmas ending by eq *)
-(**
-<<
-Zeq_add_S: (n,m:Z)`(Zs n) = (Zs m)`->`n = m`
-Zsimpl_plus_l: (n,m,p:Z)`n+m = n+p`->`m = p`
-Zplus_unit_left: (n,m:Z)`n+0 = m`->`n = m`
-Zplus_unit_right: (n,m:Z)`n = m+0`->`n = m`
->>
-*)
-
-(** Lemmas ending by Zgt *)
-(**
-<<
-Zsimpl_gt_plus_l: (n,m,p:Z)`p+n > p+m`->`n > m`
-Zsimpl_gt_plus_r: (n,m,p:Z)`n+p > m+p`->`n > m`
-Zgt_S_n: (n,p:Z)`(Zs p) > (Zs n)`->`p > n`
->>
-*)
-
-(** Lemmas ending by Zlt *)
-(**
-<<
-Zsimpl_lt_plus_l: (n,m,p:Z)`p+n < p+m`->`n < m`
-Zsimpl_lt_plus_r: (n,m,p:Z)`n+p < m+p`->`n < m`
-Zlt_S_n: (n,m:Z)`(Zs n) < (Zs m)`->`n < m`
->>
-*)
-
-(** Lemmas ending by Zle *)
-(** << Zsimpl_le_plus_l: (p,n,m:Z)`p+n <= p+m`->`n <= m`
-Zsimpl_le_plus_r: (p,n,m:Z)`n+p <= m+p`->`n <= m`
-Zle_S_n: (n,m:Z)`(Zs m) <= (Zs n)`->`m <= n` >> *)
-
-(** ** Bottom-up irreversible (syntactic) simplification *)
-
-(** Lemmas ending by Zle *)
-(**
-<<
-Zle_trans_S: (n,m:Z)`(Zs n) <= m`->`n <= m`
->>
-*)
-
-(** ** Other unclearly simplifying lemmas *)
-
-(** Lemmas ending by Zeq *)
-(**
-<<
-Zmult_eq: (x,y:Z)`x <> 0`->`y*x = 0`->`y = 0`
->>
-*)
-
-(* Lemmas ending by Zgt *)
-(**
-<<
-Zmult_gt: (x,y:Z)`x > 0`->`x*y > 0`->`y > 0`
->>
-*)
-
-(* Lemmas ending by Zlt *)
-(**
-<<
-pZmult_lt: (x,y:Z)`x > 0`->`0 < y*x`->`0 < y`
->>
-*)
-
-(* Lemmas ending by Zle *)
-(**
-<<
-Zmult_le: (x,y:Z)`x > 0`->`0 <= y*x`->`0 <= y`
-OMEGA1: (x,y:Z)`x = y`->`0 <= x`->`0 <= y`
->>
-*)
-
-
-(**********************************************************************)
-(** *        Irreversible lemmas with meta-variables                  *)
-(** To be used by EAuto                                               *)
-
-(* Hints Immediate *)
-(** Lemmas ending by eq *)
-(**
-<<
-Zle_antisym: (n,m:Z)`n <= m`->`m <= n`->`n = m`
->>
-*)
-
-(** Lemmas ending by Zge *)
-(**
-<<
-Zge_trans: (n,m,p:Z)`n >= m`->`m >= p`->`n >= p`
->>
-*)
-
-(** Lemmas ending by Zgt *)
-(**
-<<
-Zgt_trans: (n,m,p:Z)`n > m`->`m > p`->`n > p`
-Zgt_trans_S: (n,m,p:Z)`(Zs n) > m`->`m > p`->`n > p`
-Zle_gt_trans: (n,m,p:Z)`m <= n`->`m > p`->`n > p`
-Zgt_le_trans: (n,m,p:Z)`n > m`->`p <= m`->`n > p`
->>
-*)
-
-(** Lemmas ending by Zlt *)
-(**
-<<
-Zlt_trans: (n,m,p:Z)`n < m`->`m < p`->`n < p`
-Zlt_le_trans: (n,m,p:Z)`n < m`->`m <= p`->`n < p`
-Zle_lt_trans: (n,m,p:Z)`n <= m`->`m < p`->`n < p`
->>
-*)
-
-(** Lemmas ending by Zle *)
-(**
-<<
-Zle_trans: (n,m,p:Z)`n <= m`->`m <= p`->`n <= p`
->>
-*)
-
-
-(**********************************************************************)
-(** *               Unclear or too specific lemmas                    *)
-(** Not to be used ?                                                  *)
-
-(** ** Irreversible and too specific (not enough regular) *)
-
-(** Lemmas ending by Zle *)
-(**
-<<
-Zle_mult: (x,y:Z)`x > 0`->`0 <= y`->`0 <= y*x`
-Zle_mult_approx: (x,y,z:Z)`x > 0`->`z > 0`->`0 <= y`->`0 <= y*x+z`
-OMEGA6: (x,y,z:Z)`0 <= x`->`y = 0`->`0 <= x+y*z`
-OMEGA7: (x,y,z,t:Z)`z > 0`->`t > 0`->`0 <= x`->`0 <= y`->`0 <= x*z+y*t`
->>
-*)
-
-(** ** Expansion and too specific ? *)
-
-(** Lemmas ending by Zge *)
-(**
-<<
-Zge_mult_simpl: (a,b,c:Z)`c > 0`->`a*c >= b*c`->`a >= b`
->>
-*)
-
-(** Lemmas ending by Zgt *)
-(**
-<<
-Zgt_mult_simpl: (a,b,c:Z)`c > 0`->`a*c > b*c`->`a > b`
-Zgt_square_simpl: (x,y:Z)`x >= 0`->`y >= 0`->`x*x > y*y`->`x > y`
->>
-*)
-
-(** Lemmas ending by Zle *)
-(**
-<<
-Zle_mult_simpl: (a,b,c:Z)`c > 0`->`a*c <= b*c`->`a <= b`
-Zmult_le_approx: (x,y,z:Z)`x > 0`->`x > z`->`0 <= y*x+z`->`0 <= y`
->>
-*)
-
-(** ** Reversible but too specific ? *)
-
-(** Lemmas ending by Zlt *)
-(**
-<<
-Zlt_minus: (n,m:Z)`0 < m`->`n-m < n`
->>
-*)
-
-(**********************************************************************)
-(** *               Lemmas to be used as rewrite rules                *)
-(** but can also be used as hints                                     *)
-
-(** Left-to-right simplification lemmas (a symbol disappears) *)
-
-(**
-<<
-Zcompare_n_S: (n,m:Z)(Zcompare (Zs n) (Zs m))=(Zcompare n m)
-Zmin_n_n: (n:Z)`(Zmin n n) = n`
-Zmult_1_n: (n:Z)`1*n = n`
-Zmult_n_1: (n:Z)`n*1 = n`
-Zminus_plus: (n,m:Z)`n+m-n = m`
-Zle_plus_minus: (n,m:Z)`n+(m-n) = m`
-Zopp_Zopp: (x:Z)`(-(-x)) = x`
-Zero_left: (x:Z)`0+x = x`
-Zero_right: (x:Z)`x+0 = x`
-Zplus_inverse_r: (x:Z)`x+(-x) = 0`
-Zplus_inverse_l: (x:Z)`(-x)+x = 0`
-Zopp_intro: (x,y:Z)`(-x) = (-y)`->`x = y`
-Zmult_one: (x:Z)`1*x = x`
-Zero_mult_left: (x:Z)`0*x = 0`
-Zero_mult_right: (x:Z)`x*0 = 0`
-Zmult_Zopp_Zopp: (x,y:Z)`(-x)*(-y) = x*y`
->>
-*)
-
-(** Right-to-left simplification lemmas (a symbol disappears) *)
-
-(**
-<<
-Zpred_Sn: (m:Z)`m = (Zpred (Zs m))`
-Zs_pred: (n:Z)`n = (Zs (Zpred n))`
-Zplus_n_O: (n:Z)`n = n+0`
-Zmult_n_O: (n:Z)`0 = n*0`
-Zminus_n_O: (n:Z)`n = n-0`
-Zminus_n_n: (n:Z)`0 = n-n`
-Zred_factor6: (x:Z)`x = x+0`
-Zred_factor0: (x:Z)`x = x*1`
->>
-*)
-
-(** Unclear orientation (no symbol disappears) *)
-
-(**
-<<
-Zplus_n_Sm: (n,m:Z)`(Zs (n+m)) = n+(Zs m)`
-Zmult_n_Sm: (n,m:Z)`n*m+n = n*(Zs m)`
-Zmin_SS: (n,m:Z)`(Zs (Zmin n m)) = (Zmin (Zs n) (Zs m))`
-Zplus_assoc_l: (n,m,p:Z)`n+(m+p) = n+m+p`
-Zplus_assoc_r: (n,m,p:Z)`n+m+p = n+(m+p)`
-Zplus_permute: (n,m,p:Z)`n+(m+p) = m+(n+p)`
-Zplus_Snm_nSm: (n,m:Z)`(Zs n)+m = n+(Zs m)`
-Zminus_plus_simpl: (n,m,p:Z)`n-m = p+n-(p+m)`
-Zminus_Sn_m: (n,m:Z)`(Zs (n-m)) = (Zs n)-m`
-Zmult_plus_distr_l: (n,m,p:Z)`(n+m)*p = n*p+m*p`
-Zmult_minus_distr: (n,m,p:Z)`(n-m)*p = n*p-m*p`
-Zmult_assoc_r: (n,m,p:Z)`n*m*p = n*(m*p)`
-Zmult_assoc_l: (n,m,p:Z)`n*(m*p) = n*m*p`
-Zmult_permute: (n,m,p:Z)`n*(m*p) = m*(n*p)`
-Zmult_Sm_n: (n,m:Z)`n*m+m = (Zs n)*m`
-Zmult_Zplus_distr: (x,y,z:Z)`x*(y+z) = x*y+x*z`
-Zmult_plus_distr: (n,m,p:Z)`(n+m)*p = n*p+m*p`
-Zopp_Zplus: (x,y:Z)`(-(x+y)) = (-x)+(-y)`
-Zplus_sym: (x,y:Z)`x+y = y+x`
-Zplus_assoc: (x,y,z:Z)`x+(y+z) = x+y+z`
-Zmult_sym: (x,y:Z)`x*y = y*x`
-Zmult_assoc: (x,y,z:Z)`x*(y*z) = x*y*z`
-Zopp_Zmult: (x,y:Z)`(-x)*y = (-(x*y))`
-Zplus_S_n: (x,y:Z)`(Zs x)+y = (Zs (x+y))`
-Zopp_one: (x:Z)`(-x) = x*(-1)`
-Zopp_Zmult_r: (x,y:Z)`(-(x*y)) = x*(-y)`
-Zmult_Zopp_left: (x,y:Z)`(-x)*y = x*(-y)`
-Zopp_Zmult_l: (x,y:Z)`(-(x*y)) = (-x)*y`
-Zred_factor1: (x:Z)`x+x = x*2`
-Zred_factor2: (x,y:Z)`x+x*y = x*(1+y)`
-Zred_factor3: (x,y:Z)`x*y+x = x*(1+y)`
-Zred_factor4: (x,y,z:Z)`x*y+x*z = x*(y+z)`
-Zminus_Zplus_compatible: (x,y,n:Z)`x+n-(y+n) = x-y`
-Zmin_plus: (x,y,n:Z)`(Zmin (x+n) (y+n)) = (Zmin x y)+n`
->>
-*)
-
-(** nat <-> Z *)
-(**
-<<
-inj_S: (y:nat)`(inject_nat (S y)) = (Zs (inject_nat y))`
-inj_plus: (x,y:nat)`(inject_nat (plus x y)) = (inject_nat x)+(inject_nat y)`
-inj_mult: (x,y:nat)`(inject_nat (mult x y)) = (inject_nat x)*(inject_nat y)`
-inj_minus1:
- (x,y:nat)(le y x)->`(inject_nat (minus x y)) = (inject_nat x)-(inject_nat y)`
-inj_minus2: (x,y:nat)(gt y x)->`(inject_nat (minus x y)) = 0`
->>
-*)
-
-(** Too specific ? *)
-(**
-<<
-Zred_factor5: (x,y:Z)`x*0+y = y`
->>
-*)
-