diff options
author | sacerdot <sacerdot@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2004-09-03 09:27:26 +0000 |
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committer | sacerdot <sacerdot@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2004-09-03 09:27:26 +0000 |
commit | c0d7769b366e387ed9e00b05870991c4c9440f41 (patch) | |
tree | efdf089600c420336893b11d5a76294c7032e08a /contrib7 | |
parent | e4f4ddb2263c03421a8545c5e0ab20a7f52057f5 (diff) |
V7 .v files for Setoid_* and Ring over setoids commented out.
To re-enable them I would need to back-port theories/Setoids/Setoid.v from the
new syntax to the old syntax. However, since the translator is going to
be removed from the next major Coq version, I am not doing it (unless
required to).
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@6046 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'contrib7')
-rw-r--r-- | contrib7/ring/Setoid_ring_normalize.v | 76 | ||||
-rw-r--r-- | contrib7/ring/Setoid_ring_theory.v | 8 |
2 files changed, 57 insertions, 27 deletions
diff --git a/contrib7/ring/Setoid_ring_normalize.v b/contrib7/ring/Setoid_ring_normalize.v index d71c5f4c2..9aeca8d97 100644 --- a/contrib7/ring/Setoid_ring_normalize.v +++ b/contrib7/ring/Setoid_ring_normalize.v @@ -8,6 +8,7 @@ (* $Id$ *) +(* Require Setoid_ring_theory. Require Quote. @@ -43,11 +44,11 @@ Variable opp_morph : (a,a0:A) (Aequiv a a0)->(Aequiv (Aopp a) (Aopp a0)). Add Morphism Aplus : Aplus_ext. -Exact plus_morph. +Intros; Apply plus_morph; Assumption. Save. Add Morphism Amult : Amult_ext. -Exact mult_morph. +Intros; Apply mult_morph; Assumption. Save. Add Morphism Aopp : Aopp_ext. @@ -477,19 +478,22 @@ Rewrite (interp_m_ok (Aplus a a0) v0). Rewrite (interp_m_ok a v0). Rewrite (interp_m_ok a0 v0). Setoid_replace (Amult (Aplus a a0) (interp_vl v0)) - with (Aplus (Amult a (interp_vl v0)) (Amult a0 (interp_vl v0))). + with (Aplus (Amult a (interp_vl v0)) (Amult a0 (interp_vl v0))); + [ Idtac | Trivial ]. Setoid_replace (Aplus (Aplus (Amult a (interp_vl v0)) (Amult a0 (interp_vl v0))) (Aplus (interp_setcs c) (interp_setcs c0))) with (Aplus (Amult a (interp_vl v0)) (Aplus (Amult a0 (interp_vl v0)) - (Aplus (interp_setcs c) (interp_setcs c0)))). + (Aplus (interp_setcs c) (interp_setcs c0)))); + [ Idtac | Trivial ]. Setoid_replace (Aplus (Aplus (Amult a (interp_vl v0)) (interp_setcs c)) (Aplus (Amult a0 (interp_vl v0)) (interp_setcs c0))) with (Aplus (Amult a (interp_vl v0)) (Aplus (interp_setcs c) - (Aplus (Amult a0 (interp_vl v0)) (interp_setcs c0)))). + (Aplus (Amult a0 (interp_vl v0)) (interp_setcs c0)))); + [ Idtac | Trivial ]. Auto. Elim (varlist_lt v v0); Simpl. @@ -546,19 +550,22 @@ Rewrite (H c0). Rewrite (interp_m_ok (Aplus a Aone) v0). Rewrite (interp_m_ok a v0). Setoid_replace (Amult (Aplus a Aone) (interp_vl v0)) - with (Aplus (Amult a (interp_vl v0)) (Amult Aone (interp_vl v0))). + with (Aplus (Amult a (interp_vl v0)) (Amult Aone (interp_vl v0))); + [ Idtac | Trivial ]. Setoid_replace (Aplus (Aplus (Amult a (interp_vl v0)) (Amult Aone (interp_vl v0))) (Aplus (interp_setcs c) (interp_setcs c0))) with (Aplus (Amult a (interp_vl v0)) (Aplus (Amult Aone (interp_vl v0)) - (Aplus (interp_setcs c) (interp_setcs c0)))). + (Aplus (interp_setcs c) (interp_setcs c0)))); + [ Idtac | Trivial ]. Setoid_replace (Aplus (Aplus (Amult a (interp_vl v0)) (interp_setcs c)) (Aplus (interp_vl v0) (interp_setcs c0))) with (Aplus (Amult a (interp_vl v0)) (Aplus (interp_setcs c) (Aplus (interp_vl v0) (interp_setcs c0)))). -Setoid_replace (Amult Aone (interp_vl v0)) with (interp_vl v0). +Setoid_replace (Amult Aone (interp_vl v0)) with (interp_vl v0); + [ Idtac | Trivial ]. Auto. Elim (varlist_lt v v0); Simpl. @@ -620,6 +627,7 @@ Rewrite (interp_m_ok (Aplus Aone a) v0); Rewrite (interp_m_ok a v0). Setoid_replace (Amult (Aplus Aone a) (interp_vl v0)) with (Aplus (Amult Aone (interp_vl v0)) (Amult a (interp_vl v0))); + [ Idtac | Trivial ]. Setoid_replace (Aplus (Aplus (Amult Aone (interp_vl v0)) (Amult a (interp_vl v0))) @@ -627,11 +635,13 @@ Setoid_replace (Aplus with (Aplus (Amult Aone (interp_vl v0)) (Aplus (Amult a (interp_vl v0)) (Aplus (interp_setcs c) (interp_setcs c0)))); + [ Idtac | Trivial ]. Setoid_replace (Aplus (Aplus (interp_vl v0) (interp_setcs c)) (Aplus (Amult a (interp_vl v0)) (interp_setcs c0))) with (Aplus (interp_vl v0) (Aplus (interp_setcs c) - (Aplus (Amult a (interp_vl v0)) (interp_setcs c0)))). + (Aplus (Amult a (interp_vl v0)) (interp_setcs c0)))); + [ Idtac | Trivial ]. Auto. Elim (varlist_lt v v0); Simpl; Intros. @@ -684,6 +694,7 @@ H c0). Rewrite (interp_m_ok (Aplus Aone Aone) v0). Setoid_replace (Amult (Aplus Aone Aone) (interp_vl v0)) with (Aplus (Amult Aone (interp_vl v0)) (Amult Aone (interp_vl v0))); + [ Idtac | Trivial ]. Setoid_replace (Aplus (Aplus (Amult Aone (interp_vl v0)) (Amult Aone (interp_vl v0))) @@ -691,10 +702,12 @@ Setoid_replace (Aplus with (Aplus (Amult Aone (interp_vl v0)) (Aplus (Amult Aone (interp_vl v0)) (Aplus (interp_setcs c) (interp_setcs c0)))); + [ Idtac | Trivial ]. Setoid_replace (Aplus (Aplus (interp_vl v0) (interp_setcs c)) (Aplus (interp_vl v0) (interp_setcs c0))) with (Aplus (interp_vl v0) - (Aplus (interp_setcs c) (Aplus (interp_vl v0) (interp_setcs c0)))). + (Aplus (interp_setcs c) (Aplus (interp_vl v0) (interp_setcs c0)))); + [ Idtac | Trivial ]. Setoid_replace (Amult Aone (interp_vl v0)) with (interp_vl v0); Auto. Elim (varlist_lt v v0); Simpl. @@ -751,7 +764,8 @@ Rewrite (ics_aux_ok (interp_m a0 v) c). Rewrite (interp_m_ok (Aplus a a0) v); Rewrite (interp_m_ok a0 v). Setoid_replace (Amult (Aplus a a0) (interp_vl v)) - with (Aplus (Amult a (interp_vl v)) (Amult a0 (interp_vl v))). + with (Aplus (Amult a (interp_vl v)) (Amult a0 (interp_vl v))); + [ Idtac | Trivial ]. Auto. Elim (varlist_lt l v); Simpl; Intros. @@ -770,8 +784,10 @@ Rewrite (ics_aux_ok (interp_m (Aplus a Aone) v) c); Rewrite (ics_aux_ok (interp_vl v) c). Rewrite (interp_m_ok (Aplus a Aone) v). Setoid_replace (Amult (Aplus a Aone) (interp_vl v)) - with (Aplus (Amult a (interp_vl v)) (Amult Aone (interp_vl v))). -Setoid_replace (Amult Aone (interp_vl v)) with (interp_vl v). + with (Aplus (Amult a (interp_vl v)) (Amult Aone (interp_vl v))); + [ Idtac | Trivial ]. +Setoid_replace (Amult Aone (interp_vl v)) with (interp_vl v); + [ Idtac | Trivial ]. Auto. Elim (varlist_lt l v); Simpl; Intros; Auto. @@ -795,7 +811,8 @@ Rewrite (ics_aux_ok (interp_m a v) c). Rewrite (interp_m_ok (Aplus Aone a) v); Rewrite (interp_m_ok a v). Setoid_replace (Amult (Aplus Aone a) (interp_vl v)) - with (Aplus (Amult Aone (interp_vl v)) (Amult a (interp_vl v))). + with (Aplus (Amult Aone (interp_vl v)) (Amult a (interp_vl v))); + [ Idtac | Trivial ]. Setoid_replace (Amult Aone (interp_vl v)) with (interp_vl v); Auto. Elim (varlist_lt l v); Simpl; Intros; Auto. @@ -810,7 +827,8 @@ Rewrite (ics_aux_ok (interp_m (Aplus Aone Aone) v) c); Rewrite (ics_aux_ok (interp_vl v) c). Rewrite (interp_m_ok (Aplus Aone Aone) v). Setoid_replace (Amult (Aplus Aone Aone) (interp_vl v)) - with (Aplus (Amult Aone (interp_vl v)) (Amult Aone (interp_vl v))). + with (Aplus (Amult Aone (interp_vl v)) (Amult Aone (interp_vl v))); + [ Idtac | Trivial ]. Setoid_replace (Amult Aone (interp_vl v)) with (interp_vl v); Auto. Elim (varlist_lt l v); Simpl; Intros; Auto. @@ -832,7 +850,8 @@ Rewrite (interp_m_ok (Amult a a0) v); Rewrite (interp_m_ok a0 v). Rewrite H. Setoid_replace (Amult a (Aplus (Amult a0 (interp_vl v)) (interp_setcs c))) - with (Aplus (Amult a (Amult a0 (interp_vl v))) (Amult a (interp_setcs c))). + with (Aplus (Amult a (Amult a0 (interp_vl v))) (Amult a (interp_setcs c))); + [ Idtac | Trivial ]. Auto. Rewrite (ics_aux_ok (interp_m a v) (canonical_sum_scalar a c)); @@ -854,7 +873,8 @@ Rewrite (varlist_merge_ok l v). Setoid_replace (Amult (interp_vl l) (Aplus (Amult a (interp_vl v)) (interp_setcs c))) with (Aplus (Amult (interp_vl l) (Amult a (interp_vl v))) - (Amult (interp_vl l) (interp_setcs c))). + (Amult (interp_vl l) (interp_setcs c))); + [ Idtac | Trivial ]. Auto. Rewrite (varlist_insert_ok (varlist_merge l v) @@ -881,14 +901,17 @@ Rewrite (varlist_merge_ok l v). Setoid_replace (Amult (interp_vl l) (Aplus (Amult a (interp_vl v)) (interp_setcs c0))) with (Aplus (Amult (interp_vl l) (Amult a (interp_vl v))) - (Amult (interp_vl l) (interp_setcs c0))). + (Amult (interp_vl l) (interp_setcs c0))); + [ Idtac | Trivial ]. Setoid_replace (Amult c (Aplus (Amult (interp_vl l) (Amult a (interp_vl v))) (Amult (interp_vl l) (interp_setcs c0)))) with (Aplus (Amult c (Amult (interp_vl l) (Amult a (interp_vl v)))) - (Amult c (Amult (interp_vl l) (interp_setcs c0)))). + (Amult c (Amult (interp_vl l) (interp_setcs c0)))); + [ Idtac | Trivial ]. Setoid_replace (Amult (Amult c a) (Amult (interp_vl l) (interp_vl v))) - with (Amult c (Amult a (Amult (interp_vl l) (interp_vl v)))). + with (Amult c (Amult a (Amult (interp_vl l) (interp_vl v)))); + [ Idtac | Trivial ]. Auto. Rewrite (monom_insert_ok c (varlist_merge l v) @@ -900,7 +923,8 @@ Setoid_replace (Aplus (Amult c (Amult (interp_vl l) (interp_vl v))) (Amult c (Amult (interp_vl l) (interp_setcs c0)))) with (Amult c (Aplus (Amult (interp_vl l) (interp_vl v)) - (Amult (interp_vl l) (interp_setcs c0)))). + (Amult (interp_vl l) (interp_setcs c0)))); + [ Idtac | Trivial ]. Auto. Save. @@ -917,11 +941,13 @@ Rewrite (ics_aux_ok (interp_m a v) c). Rewrite (interp_m_ok a v). Rewrite (H y). Setoid_replace (Amult a (Amult (interp_vl v) (interp_setcs y))) - with (Amult (Amult a (interp_vl v)) (interp_setcs y)). + with (Amult (Amult a (interp_vl v)) (interp_setcs y)); + [ Idtac | Trivial ]. Setoid_replace (Amult (Aplus (Amult a (interp_vl v)) (interp_setcs c)) (interp_setcs y)) with (Aplus (Amult (Amult a (interp_vl v)) (interp_setcs y)) - (Amult (interp_setcs c) (interp_setcs y))). + (Amult (interp_setcs c) (interp_setcs y))); + [ Idtac | Trivial ]. Trivial. Rewrite (canonical_sum_merge_ok (canonical_sum_scalar2 v y) @@ -958,7 +984,8 @@ Intros. Rewrite (ics_aux_ok (interp_m a v) c). Rewrite (interp_m_ok a v). Rewrite (H0 I). -Setoid_replace (Amult Azero (interp_vl v)) with Azero. +Setoid_replace (Amult Azero (interp_vl v)) with Azero; + [ Idtac | Trivial ]. Rewrite H. Trivial. @@ -1139,3 +1166,4 @@ Save. End setoid_rings. End setoid. +*) diff --git a/contrib7/ring/Setoid_ring_theory.v b/contrib7/ring/Setoid_ring_theory.v index 240343963..e152130ae 100644 --- a/contrib7/ring/Setoid_ring_theory.v +++ b/contrib7/ring/Setoid_ring_theory.v @@ -8,6 +8,7 @@ (* $Id$ *) +(* Require Export Bool. Require Export Setoid. @@ -42,15 +43,15 @@ Variable mult_morph : (a,a0,a1,a2:A) a == a0 -> a1 == a2 -> a*a1 == a0*a2. Variable opp_morph : (a,a0:A) a == a0 -> -a == -a0. Add Morphism Aplus : Aplus_ext. -Exact plus_morph. +Intros; Apply plus_morph; Assumption. Save. Add Morphism Amult : Amult_ext. -Exact mult_morph. +Intros; Apply mult_morph; Assumption. Save. Add Morphism Aopp : Aopp_ext. -Exact opp_morph. +Intros; Apply opp_morph; Assumption. Save. Section Theory_of_semi_setoid_rings. @@ -427,3 +428,4 @@ Section power_ring. End power_ring. End Setoid_rings. +*) |