diff options
| author |  Matthieu Sozeau <matthieu.sozeau@inria.fr> | 2014-09-25 00:12:26 +0200 |
|---|---|---|
| committer | Matthieu Sozeau <matthieu.sozeau@inria.fr> | 2014-09-27 21:56:58 +0200 |
| commit | 3fe4912b568916676644baeb982a3e10c592d887 (patch) | |
| tree | 291c25d55d62c94af8fc3eb5a6d6df1150bc893f /plugins/setoid_ring/Field_theory.v | |
| parent | a95210435f336d89f44052170a7c65563e6e35f2 (diff) | |
Keyed unification option, compiling the whole standard library
(but deactivated still).
Set Keyed Unification to activate the option, which changes
subterm selection to _always_ use full conversion _after_ finding a
subterm whose head/key matches the key of the term we're looking for.
This applies to rewrite and higher-order unification in
apply/elim/destruct.
Most proof scripts already abide by these semantics. For those that
don't, it's usually only a matter of using:
Declare Equivalent Keys f g.
This make keyed unification consider f and g to match as keys.
This takes care of most cases of abbreviations: typically Def foo :=
bar and rewriting with a bar-headed lhs in a goal mentioning foo works
once they're set equivalent.
For canonical structures, these hints should be automatically declared.
For non-global-reference headed terms, the key is the constructor name
(Sort, Prod...). Evars and metas are no keys.
INCOMPATIBILITIES:
In FMapFullAVL, a Function definition doesn't go through with keyed
unification on.
Diffstat (limited to 'plugins/setoid_ring/Field_theory.v')
| -rw-r--r-- | plugins/setoid_ring/Field_theory.v | 9 |
1 files changed, 6 insertions, 3 deletions
diff --git a/plugins/setoid_ring/Field_theory.v b/plugins/setoid_ring/Field_theory.v index ad7fbd871..16f9b9723 100644 --- a/plugins/setoid_ring/Field_theory.v +++ b/plugins/setoid_ring/Field_theory.v @@ -1168,7 +1168,8 @@ induction fe; simpl condition; rewrite ?PCond_cons, ?PCond_app; simpl; assert (U2 := split_ok_r (num F1) (num F2) l). assert (U3 := split_ok_l (denum F1) (denum F2) l). assert (U4 := split_ok_r (denum F1) (denum F2) l). - rewrite (IHfe1 Hc2), (IHfe2 Hc3), U1, U2, U3, U4; apply rdiv7b; + rewrite (IHfe1 Hc2), (IHfe2 Hc3), U1, U2, U3, U4. + simpl in U2, U3, U4. apply rdiv7b; rewrite <- ?U2, <- ?U3, <- ?U4; try apply Pcond_Fnorm; trivial. - rewrite !NPEpow_ok. simpl. rewrite !rpow_pow, (IHfe Hc). @@ -1274,6 +1275,9 @@ Qed. (* simplify a field equation : generate the crossproduct and simplify polynomials *) +(** This allows rewriting modulo the simplification of PEeval on PMul *) +Declare Equivalent Keys PEeval rmul. + Theorem Field_simplify_eq_correct : forall n l lpe fe1 fe2, Ninterp_PElist l lpe -> @@ -1294,8 +1298,7 @@ rewrite (split_ok_r (denum nfe1) (denum nfe2) l), eq3. simpl. rewrite !rmul_assoc. apply rmul_ext; trivial. -rewrite - (ring_rw_correct n lpe l Hlpe Logic.eq_refl (num nfe1 * right den) Logic.eq_refl), +rewrite (ring_rw_correct n lpe l Hlpe Logic.eq_refl (num nfe1 * right den) Logic.eq_refl), (ring_rw_correct n lpe l Hlpe Logic.eq_refl (num nfe2 * left den) Logic.eq_refl). rewrite Hlmp. apply Hcrossprod. |