wip tactics

Tactics.v

@@ -74,7 +74,9 @@ Theorem silly_ex :
      oddb 3 = true ->
      evenb 4 = true.
 Proof.
-  (* FILL IN HERE *) Admitted.
+  intros A B.
+  apply B.
+Qed.
 (** [] *)
 
 (** To use the [apply] tactic, the (conclusion of the) fact
@@ -107,8 +109,11 @@ Theorem rev_exercise1 : forall (l l' : list nat),
      l = rev l' ->
      l' = rev l.
 Proof.
-  (* FILL IN HERE *) Admitted.
+  intros l l' H.
-(** [] *)
+  rewrite -> H.
+  symmetry.
+  apply rev_involutive.
+Qed.
 
 (** **** Exercise: 1 star, standard, optional (apply_rewrite)  
 
@@ -176,8 +181,10 @@ Example trans_eq_exercise : forall (n m o p : nat),
      (n + p) = m ->
      (n + p) = (minustwo o).
 Proof.
-  (* FILL IN HERE *) Admitted.
+  intros n m o p H J.
-(** [] *)
+  apply trans_eq with (m:=m).
+  apply J. apply H.
+Qed.
 
 (* ################################################################# *)
 (** * The [injection] and [discriminate] Tactics *)
@@ -273,8 +280,9 @@ Example injection_ex3 : forall (X : Type) (x y z : X) (l j : list X),
   y :: l = x :: j ->
   x = y.
 Proof.
-  (* FILL IN HERE *) Admitted.
+  intros X x y z l j H J.
-(** [] *)
+  injection J as J1. symmetry. apply J1.
+Qed.
 
 (** So much for injectivity of constructors.  What about disjointness?
 
@@ -345,8 +353,9 @@ Example discriminate_ex3 :
     x :: y :: l = [] ->
     x = z.
 Proof.
-  (* FILL IN HERE *) Admitted.
+  intros X x y z l H J.
-(** [] *)
+  discriminate J.
+Qed.
 
 (** The injectivity of constructors allows us to reason that
     [forall (n m : nat), S n = S m -> n = m].  The converse of this