diff --git a/doc/examples/bintree.lean b/doc/examples/bintree.lean index 46c09e333d..37622c710e 100644 --- a/doc/examples/bintree.lean +++ b/doc/examples/bintree.lean @@ -105,10 +105,11 @@ The proof of the auxiliary theorem is by induction on `t`\ . The `generalizing acc` modifier instructs Lean to revert `acc`\ , apply the induction theorem for `Tree`\ s, and then reintroduce `acc` in each case. By using `generalizing`\ , we obtain the more general induction hypotheses -```lean -left_ih : ∀ acc, toListTR.go left acc = toList left ++ acc -right_ih : ∀ acc, toListTR.go right acc = toList right ++ acc -``` + +- `left_ih : ∀ acc, toListTR.go left acc = toList left ++ acc` + +- `right_ih : ∀ acc, toListTR.go right acc = toList right ++ acc` + Recall that the combinator `tac <;> tac'` runs `tac` on the main goal and `tac'` on each produced goal, concatenating all goals produced by `tac'`\ . In this theorem, we use it to apply `simp` and close each subgoal produced by the `induction` tactic.