X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=weblib%2Ftutorial%2Fchapter1.ma;h=9043bdad712795d8f6f76104e72d4dc6601a3455;hb=a2ba04cd90e76937720b16e37cb12a39b46181e3;hp=6598df5c14a13dede5438c154a5f2b398e853a7f;hpb=bf776a7d58bdee34f479e3236f7c220bdfca669a;p=helm.git

diff --git a/weblib/tutorial/chapter1.ma b/weblib/tutorial/chapter1.ma
index 6598df5c1..9043bdad7 100644
--- a/weblib/tutorial/chapter1.ma
+++ b/weblib/tutorial/chapter1.ma
@@ -23,7 +23,8 @@ computational mechanism based on the declaration of inductive types.
 Let us start this tutorial with a simple example based on the following well 
 known problem.
 
-h2 class="section"The goat, the wolf and the cabbage/h2A farmer need to transfer a goat, a wolf and a cabbage across a river, but there
+h2 class="section"The goat, the wolf and the cabbage/h2
+A farmer need to transfer a goat, a wolf and a cabbage across a river, but there
 is only one place available on his boat. Furthermore, the goat will eat the 
 cabbage if they are left alone on the same bank, and similarly the wolf will eat
 the goat. The problem consists in bringing all three items safely across the 
@@ -148,7 +149,8 @@ inductive opp : a href="cic:/matita/tutorial/chapter1/bank.ind(1,0,0)"bank/a
 (* In precisely the same way as "bank" is the smallest type containing east and
 west, opp is the smallest predicate containing the two sub-cases east_west and
 weast_east. If you have some familiarity with Prolog, you may look at opp as the
-predicate definined by the two clauses - in this case, the two facts -
+predicate defined by the two clauses - in this case, the two facts - ast_west and
+west_east.
 
 Between opp and opposite we have the following relation:
     opp a b iff a = opposite b
@@ -211,11 +213,8 @@ of a relation (a binary predicate) over states. *)
 
 inductive move : a href="cic:/matita/tutorial/chapter1/state.ind(1,0,0)"state/a → a href="cic:/matita/tutorial/chapter1/state.ind(1,0,0)"state/a → Prop ≝
 | move_goat: ∀g,g1,w,c. a href="cic:/matita/tutorial/chapter1/opp.ind(1,0,0)"opp/a g g1 → move (a href="cic:/matita/tutorial/chapter1/state.con(0,1,0)"mk_state/a g w c g) (a href="cic:/matita/tutorial/chapter1/state.con(0,1,0)"mk_state/a g1 w c g1)
-         (* Every time g and g1 are two opposite banks, it is legal to put
-                the state "a href="cic:/matita/tutorial/chapter1/state.con(0,1,0)"mk_state/a g w c g", which says that goat and boat are on the same bank g,
-            and the state "a href="cic:/matita/tutorial/chapter1/state.con(0,1,0)"mk_state/a g1 w c g1", which says that goat and boat are on the same bank g1
-            in the relation "move" because, for example, moving the goat from bank g to bank g1 requires
-            moving the boat as well. *) 
+  (* We can move the goat from a bank g to the opposite bank g1 if and only if the
+     boat is on the same bank g of the goat and we move the boat along with it. *)
 | move_wolf: ∀g,w,w1,c. a href="cic:/matita/tutorial/chapter1/opp.ind(1,0,0)"opp/a w w1 → move (a href="cic:/matita/tutorial/chapter1/state.con(0,1,0)"mk_state/a g w c w) (a href="cic:/matita/tutorial/chapter1/state.con(0,1,0)"mk_state/a g w1 c w1)
 | move_cabbage: ∀g,w,c,c1.a href="cic:/matita/tutorial/chapter1/opp.ind(1,0,0)"opp/a c c1 → move (a href="cic:/matita/tutorial/chapter1/state.con(0,1,0)"mk_state/a g w c c) (a href="cic:/matita/tutorial/chapter1/state.con(0,1,0)"mk_state/a g w c1 c1)
 | move_boat: ∀g,w,c,b,b1. a href="cic:/matita/tutorial/chapter1/opp.ind(1,0,0)"opp/a b b1 → move (a href="cic:/matita/tutorial/chapter1/state.con(0,1,0)"mk_state/a g w c b) (a href="cic:/matita/tutorial/chapter1/state.con(0,1,0)"mk_state/a g w c b1).
@@ -244,7 +243,7 @@ need a few more applications to handle reachability, and side conditions.
 The magic number to let automation work is, in this case, 9.  *)
 
 lemma problem: a href="cic:/matita/tutorial/chapter1/reachable.ind(1,0,0)"reachable/a a href="cic:/matita/tutorial/chapter1/start.def(1)"start/a a href="cic:/matita/tutorial/chapter1/end.def(1)"end/a.
-normalize /9/ qed. 
+normalize /span class="autotactic"9span class="autotrace" trace a href="cic:/matita/tutorial/chapter1/reachable.con(0,1,0)"one/a, a href="cic:/matita/tutorial/chapter1/reachable.con(0,2,0)"more/a, a href="cic:/matita/tutorial/chapter1/safe_state.con(0,1,0)"with_boat/a, a href="cic:/matita/tutorial/chapter1/safe_state.con(0,2,0)"opposite_side/a, a href="cic:/matita/tutorial/chapter1/move.con(0,1,0)"move_goat/a, a href="cic:/matita/tutorial/chapter1/move.con(0,2,0)"move_wolf/a, a href="cic:/matita/tutorial/chapter1/move.con(0,3,0)"move_cabbage/a, a href="cic:/matita/tutorial/chapter1/move.con(0,4,0)"move_boat/a, a href="cic:/matita/tutorial/chapter1/opp.con(0,1,0)"east_west/a, a href="cic:/matita/tutorial/chapter1/opp.con(0,2,0)"west_east/a/span/span/ qed. 
 
 (* Let us now try to derive the proof in a more interactive way. Of course, we
 expect to need several moves to transfer all items from a bank to the other, so 
@@ -305,7 +304,7 @@ requires /2/ since move_goat opens an additional subgoal. By applying "]" we
 refocus on the skipped goal, going back to a situation similar to the one we
 started with. *)
 
-  | /2/ ] 
+  | /span class="autotactic"2span class="autotrace" trace a href="cic:/matita/tutorial/chapter1/move.con(0,1,0)"move_goat/a, a href="cic:/matita/tutorial/chapter1/opp.con(0,1,0)"east_west/a/span/span/ ] 
 
 (* Let us perform the next step, namely moving back the boat, in a sligtly 
 different way. The more operation expects as second argument the new 
@@ -320,7 +319,7 @@ the system. *)
 trivial. Wespan style="font-family: Verdana,sans-serif;" /spancan just apply automation to all of them, and it will close the two
 trivial goals. *)
 
-/2/
+/span class="autotactic"2span class="autotrace" trace a href="cic:/matita/tutorial/chapter1/safe_state.con(0,2,0)"opposite_side/a, a href="cic:/matita/tutorial/chapter1/move.con(0,4,0)"move_boat/a, a href="cic:/matita/tutorial/chapter1/opp.con(0,1,0)"east_west/a, a href="cic:/matita/tutorial/chapter1/opp.con(0,2,0)"west_east/a/span/span/
 
 (* Let us come to the next step, that consists in moving the wolf. Suppose that 
 instead of specifying the next intermediate state, we prefer to specify the next 
@@ -339,12 +338,12 @@ be arbitrary). The simplest way to proceed is to focus on the bank, that is
 the fourth subgoal, and explicitly instatiate it. Instead of repeatedly using "|",
 we can perform focusing by typing "4:" as described by the following command. *)
 
-[4: @a href="cic:/matita/tutorial/chapter1/bank.con(0,1,0)"east/a] /2/
+[4: @a href="cic:/matita/tutorial/chapter1/bank.con(0,1,0)"east/a] /span class="autotactic"2span class="autotrace" trace a href="cic:/matita/tutorial/chapter1/safe_state.con(0,1,0)"with_boat/a, a href="cic:/matita/tutorial/chapter1/opp.con(0,1,0)"east_west/a/span/span/
 
 (* Alternatively, we can directly instantiate the bank into the move. Let
 us complete the proof in this, very readable way. *)
 
-@(a href="cic:/matita/tutorial/chapter1/reachable.con(0,2,0)"more/a … (a href="cic:/matita/tutorial/chapter1/move.con(0,1,0)"move_goat/a a href="cic:/matita/tutorial/chapter1/bank.con(0,2,0)"west/a … )) /2/
-@(a href="cic:/matita/tutorial/chapter1/reachable.con(0,2,0)"more/a … (a href="cic:/matita/tutorial/chapter1/move.con(0,3,0)"move_cabbage/a ?? a href="cic:/matita/tutorial/chapter1/bank.con(0,1,0)"east/a … )) /2/
-@(a href="cic:/matita/tutorial/chapter1/reachable.con(0,2,0)"more/a … (a href="cic:/matita/tutorial/chapter1/move.con(0,4,0)"move_boat/a ??? a href="cic:/matita/tutorial/chapter1/bank.con(0,2,0)"west/a … )) /2/
-@a href="cic:/matita/tutorial/chapter1/reachable.con(0,1,0)"one/a /2/ qed.
\ No newline at end of file
+@(a href="cic:/matita/tutorial/chapter1/reachable.con(0,2,0)"more/a … (a href="cic:/matita/tutorial/chapter1/move.con(0,1,0)"move_goat/a a href="cic:/matita/tutorial/chapter1/bank.con(0,2,0)"west/a … )) /span class="autotactic"2span class="autotrace" trace a href="cic:/matita/tutorial/chapter1/safe_state.con(0,1,0)"with_boat/a, a href="cic:/matita/tutorial/chapter1/opp.con(0,2,0)"west_east/a/span/span/
+@(a href="cic:/matita/tutorial/chapter1/reachable.con(0,2,0)"more/a … (a href="cic:/matita/tutorial/chapter1/move.con(0,3,0)"move_cabbage/a ?? a href="cic:/matita/tutorial/chapter1/bank.con(0,1,0)"east/a … )) /span class="autotactic"2span class="autotrace" trace a href="cic:/matita/tutorial/chapter1/safe_state.con(0,2,0)"opposite_side/a, a href="cic:/matita/tutorial/chapter1/opp.con(0,1,0)"east_west/a, a href="cic:/matita/tutorial/chapter1/opp.con(0,2,0)"west_east/a/span/span/
+@(a href="cic:/matita/tutorial/chapter1/reachable.con(0,2,0)"more/a … (a href="cic:/matita/tutorial/chapter1/move.con(0,4,0)"move_boat/a ??? a href="cic:/matita/tutorial/chapter1/bank.con(0,2,0)"west/a … )) /span class="autotactic"2span class="autotrace" trace a href="cic:/matita/tutorial/chapter1/safe_state.con(0,1,0)"with_boat/a, a href="cic:/matita/tutorial/chapter1/opp.con(0,2,0)"west_east/a/span/span/
+@a href="cic:/matita/tutorial/chapter1/reachable.con(0,1,0)"one/a /span class="autotactic"2span class="autotrace" trace a href="cic:/matita/tutorial/chapter1/move.con(0,1,0)"move_goat/a, a href="cic:/matita/tutorial/chapter1/opp.con(0,1,0)"east_west/a/span/span/ qed.
\ No newline at end of file