diff options
author | herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2008-12-29 17:15:52 +0000 |
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committer | herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2008-12-29 17:15:52 +0000 |
commit | b18a6d179903546cbf5745e601ab221f06e30078 (patch) | |
tree | c9ed543e785c2bcfad768669812778a9d3aea33e /theories/ZArith/auxiliary.v | |
parent | f34f0420899594847b6e7633a4488f034a4300f6 (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.v | 40 |
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. |