and_then is subtly different from <;>. The former focuses the goal, whereas the latter does not.

[alexkeizer]

Page 60 suggests that a and_then b behaves the same as a <;> b, but this is not the case when b does not close all goals;

For example, if the second tactic is skip. The <;> version compiles just fine.

example {x : Nat} : True :=
by
  cases x <;> skip
  repeat exact True.intro

But, the and_then version complains about unsolved goals.

macro a:tactic " and_then " b:tactic : tactic =>
    `(tactic|  $a:tactic; all_goals $b:tactic)

example {x : Nat} : true :=
by
  cases x and_then skip -- Error: unsolved goals ...
  repeat exact True.intro

I don't readily see how to fix this while keeping it as a simple substitution-macro, but maybe this discrepancy should be pointed out in the text.

[arthurpaulino]

The problem was that { $a:tactic; all_goals $b:tactic }, with curly braces, was explicitly requiring it to close the goals. Removing them solved the problem.

Commit link

[alexkeizer]

We still want to focus the main goal, before applying a, so that b only works on those goals introduced by a.

example {x y : Nat} : y = 0 ∨ y ≠ 0 :=
by
  cases y;
  cases x and_then {
    apply Or.inl;
    rfl
  }
  apply Or.inr
  simp

Turns out focus does exactly that, so the macro should be

macro a:tactic " and_then " b:tactic : tactic =>
    `(tactic| 
        focus 
          $a:tactic; all_goals $b:tactic
      )

I'd make a PR, but that seems a bit overkill for a change this tiny?

[arthurpaulino]

@alexkeizer the PR is highly welcome if you explain the change in the text. We're in the tactics chapter afterall 👍🏼