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authorGravatar herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7>2008-12-29 17:15:52 +0000
committerGravatar herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7>2008-12-29 17:15:52 +0000
commitb18a6d179903546cbf5745e601ab221f06e30078 (patch)
treec9ed543e785c2bcfad768669812778a9d3aea33e /theories/ZArith/auxiliary.v
parentf34f0420899594847b6e7633a4488f034a4300f6 (diff)
- Added support for subterm matching in SearchAbout.
- Backtrack on precise unfolding of "iff" in "tauto": it has effects on the naming of hypotheses (especially when doing "case H" with H of type "{x|P<->Q}" since not unfolding will eventually introduce a name "i" while unfolding will eventually introduce a name "a" (deep sigh). - Miscellaneous (error when a plugin is missing, doc hnf, standardization of names manipulating type constr_pattern, ...). git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@11725 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/ZArith/auxiliary.v')
-rw-r--r--theories/ZArith/auxiliary.v40
1 files changed, 0 insertions, 40 deletions
diff --git a/theories/ZArith/auxiliary.v b/theories/ZArith/auxiliary.v
index 18b49f4bb..5edf68013 100644
--- a/theories/ZArith/auxiliary.v
+++ b/theories/ZArith/auxiliary.v
@@ -91,46 +91,6 @@ Proof.
rewrite Zplus_opp_r; trivial.
Qed.
-(**********************************************************************)
-(** * Factorization lemmas *)
-
-Theorem Zred_factor0 : forall n:Z, n = n * 1.
- intro x; rewrite (Zmult_1_r x); reflexivity.
-Qed.
-
-Theorem Zred_factor1 : forall n:Z, n + n = n * 2.
-Proof.
- exact Zplus_diag_eq_mult_2.
-Qed.
-
-Theorem Zred_factor2 : forall n m:Z, n + n * m = n * (1 + m).
-Proof.
- intros x y; pattern x at 1 in |- *; rewrite <- (Zmult_1_r x);
- rewrite <- Zmult_plus_distr_r; trivial with arith.
-Qed.
-
-Theorem Zred_factor3 : forall n m:Z, n * m + n = n * (1 + m).
-Proof.
- intros x y; pattern x at 2 in |- *; rewrite <- (Zmult_1_r x);
- rewrite <- Zmult_plus_distr_r; rewrite Zplus_comm;
- trivial with arith.
-Qed.
-
-Theorem Zred_factor4 : forall n m p:Z, n * m + n * p = n * (m + p).
-Proof.
- intros x y z; symmetry in |- *; apply Zmult_plus_distr_r.
-Qed.
-
-Theorem Zred_factor5 : forall n m:Z, n * 0 + m = m.
-Proof.
- intros x y; rewrite <- Zmult_0_r_reverse; auto with arith.
-Qed.
-
-Theorem Zred_factor6 : forall n:Z, n = n + 0.
-Proof.
- intro; rewrite Zplus_0_r; trivial with arith.
-Qed.
-
Theorem Zle_mult_approx :
forall n m p:Z, n > 0 -> p > 0 -> 0 <= m -> 0 <= m * n + p.
Proof.