diff options
Diffstat (limited to 'theories')
| -rw-r--r-- | theories/ZArith/Zlogarithm.v | 15 |
1 files changed, 7 insertions, 8 deletions
diff --git a/theories/ZArith/Zlogarithm.v b/theories/ZArith/Zlogarithm.v index 18d1bba97..68e9c7733 100644 --- a/theories/ZArith/Zlogarithm.v +++ b/theories/ZArith/Zlogarithm.v @@ -54,20 +54,19 @@ Section Log_pos. (* Log of positive integers *) Theorem log_inf_correct : forall x:positive, 0 <= log_inf x /\ two_p (log_inf x) <= Zpos x < two_p (Zsucc (log_inf x)). + Proof. simple induction x; intros; simpl in |- *; [ elim H; intros Hp HR; clear H; split; [ auto with zarith - | conditional apply Zle_le_succ; trivial rewrite - two_p_S with (x := Zsucc (log_inf p)); - conditional trivial rewrite two_p_S; - conditional trivial rewrite two_p_S in HR; rewrite (BinInt.Zpos_xI p); + | rewrite two_p_S with (x := Zsucc (log_inf p)) by (apply Zle_le_succ; trivial); + rewrite two_p_S by trivial; + rewrite two_p_S in HR by trivial; rewrite (BinInt.Zpos_xI p); omega ] | elim H; intros Hp HR; clear H; split; [ auto with zarith - | conditional apply Zle_le_succ; trivial rewrite - two_p_S with (x := Zsucc (log_inf p)); - conditional trivial rewrite two_p_S; - conditional trivial rewrite two_p_S in HR; rewrite (BinInt.Zpos_xO p); + | rewrite two_p_S with (x := Zsucc (log_inf p)) by (apply Zle_le_succ; trivial); + rewrite two_p_S by trivial; + rewrite two_p_S in HR by trivial; rewrite (BinInt.Zpos_xO p); omega ] | unfold two_power_pos in |- *; unfold shift_pos in |- *; simpl in |- *; omega ]. |