diff options
| author |  Emilio Jesus Gallego Arias <e+git@x80.org> | 2018-04-09 01:33:31 +0200 |
|---|---|---|
| committer | Emilio Jesus Gallego Arias <e+git@x80.org> | 2018-04-13 12:13:48 +0200 |
| commit | 2243c25c79ab19876ad74452c9cecc7dcc88c67c (patch) | |
| tree | f32573eb7d7c4dbdb4493e186bed87c80e61a747 /theories/Arith | |
| parent | b68e0b4f9ba37d1c2fa5921e1d934b4b38bfdfe7 (diff) | |
[ltac] Deprecate nameless fix/cofix.
LTAC's `fix` and `cofix` do require access to the proof object inside
the tactic monad when used without a name. This is a bit inconvenient
as we aim to make the handling of the proof object purely functional.
Alternatives have been discussed in #7196, and it seems that
deprecating the nameless forms may have the best cost/benefit ratio,
so opening this PR for discussion.
See also #6171.
Diffstat (limited to 'theories/Arith')
| -rw-r--r-- | theories/Arith/Div2.v | 4 | ||||
| -rw-r--r-- | theories/Arith/Even.v | 4 | ||||
| -rw-r--r-- | theories/Arith/PeanoNat.v | 10 |
3 files changed, 9 insertions, 9 deletions
diff --git a/theories/Arith/Div2.v b/theories/Arith/Div2.v index 42956c475..a5e457831 100644 --- a/theories/Arith/Div2.v +++ b/theories/Arith/Div2.v @@ -30,7 +30,7 @@ Lemma ind_0_1_SS : P 0 -> P 1 -> (forall n, P n -> P (S (S n))) -> forall n, P n. Proof. intros P H0 H1 H2. - fix 1. + fix ind_0_1_SS 1. destruct n as [|[|n]]. - exact H0. - exact H1. @@ -105,7 +105,7 @@ Hint Resolve double_S: arith. Lemma even_odd_double n : (even n <-> n = double (div2 n)) /\ (odd n <-> n = S (double (div2 n))). Proof. - revert n. fix 1. destruct n as [|[|n]]. + revert n. fix even_odd_double 1. destruct n as [|[|n]]. - (* n = 0 *) split; split; auto with arith. inversion 1. - (* n = 1 *) diff --git a/theories/Arith/Even.v b/theories/Arith/Even.v index baf119732..a1d0e9fcc 100644 --- a/theories/Arith/Even.v +++ b/theories/Arith/Even.v @@ -38,7 +38,7 @@ Hint Constructors odd: arith. Lemma even_equiv : forall n, even n <-> Nat.Even n. Proof. - fix 1. + fix even_equiv 1. destruct n as [|[|n]]; simpl. - split; [now exists 0 | constructor]. - split. @@ -52,7 +52,7 @@ Qed. Lemma odd_equiv : forall n, odd n <-> Nat.Odd n. Proof. - fix 1. + fix odd_equiv 1. destruct n as [|[|n]]; simpl. - split. + inversion_clear 1. diff --git a/theories/Arith/PeanoNat.v b/theories/Arith/PeanoNat.v index 4e4938a99..bc58995fd 100644 --- a/theories/Arith/PeanoNat.v +++ b/theories/Arith/PeanoNat.v @@ -315,7 +315,7 @@ Import Private_Parity. Lemma even_spec : forall n, even n = true <-> Even n. Proof. - fix 1. + fix even_spec 1. destruct n as [|[|n]]; simpl. - split; [ now exists 0 | trivial ]. - split; [ discriminate | intro H; elim (Even_1 H) ]. @@ -325,7 +325,7 @@ Qed. Lemma odd_spec : forall n, odd n = true <-> Odd n. Proof. unfold odd. - fix 1. + fix odd_spec 1. destruct n as [|[|n]]; simpl. - split; [ discriminate | intro H; elim (Odd_0 H) ]. - split; [ now exists 0 | trivial ]. @@ -473,7 +473,7 @@ Notation "( x | y )" := (divide x y) (at level 0) : nat_scope. Lemma gcd_divide : forall a b, (gcd a b | a) /\ (gcd a b | b). Proof. - fix 1. + fix gcd_divide 1. intros [|a] b; simpl. split. now exists 0. @@ -502,7 +502,7 @@ Qed. Lemma gcd_greatest : forall a b c, (c|a) -> (c|b) -> (c|gcd a b). Proof. - fix 1. + fix gcd_greatest 1. intros [|a] b; simpl; auto. fold (b mod (S a)). intros c H H'. apply gcd_greatest; auto. @@ -536,7 +536,7 @@ Qed. Lemma le_div2 n : div2 (S n) <= n. Proof. revert n. - fix 1. + fix le_div2 1. destruct n; simpl; trivial. apply lt_succ_r. destruct n; [simpl|]; trivial. now constructor. Qed. |