commit by user andrea

[helm.git] / weblib / basics / bool.ma

diff --git a/weblib/basics/bool.ma b/weblib/basics/bool.ma
index 43f0f8d051a16c388c1599f59ee7c649e24128ff..7762657aec90514366049386a6453b8f275ec1e8 100644 (file)
--- a/weblib/basics/bool.ma
+++ b/weblib/basics/bool.ma
@@ -16,7 +16,6 @@ include "basics/relations.ma".
   | true : bool
   | false : bool.
 
-(* destruct does not work *)
 \ 5img class="anchor" src="icons/tick.png" id="not_eq_true_false"\ 6theorem not_eq_true_false : \ 5a href="cic:/matita/basics/bool/bool.con(0,1,0)"\ 6true\ 5/a\ 6 \ 5a title="leibnitz's non-equality" href="cic:/fakeuri.def(1)"\ 6≠\ 5/a\ 6 \ 5a href="cic:/matita/basics/bool/bool.con(0,2,0)"\ 6false\ 5/a\ 6.
 @\ 5a href="cic:/matita/basics/logic/Not.con(0,1,1)"\ 6nmk\ 5/a\ 6 #Heq change with match \ 5a href="cic:/matita/basics/bool/bool.con(0,1,0)"\ 6true\ 5/a\ 6 with [true ⇒ \ 5a href="cic:/matita/basics/logic/False.ind(1,0,0)"\ 6False\ 5/a\ 6|false ⇒ \ 5a href="cic:/matita/basics/logic/True.ind(1,0,0)"\ 6True\ 5/a\ 6]
 >Heq // qed.
@@ -55,6 +54,10 @@ interpretation "boolean and" 'and x y = (andb x y).
 match b1 with [ true ⇒ P b2 | false ⇒ P \ 5a href="cic:/matita/basics/bool/bool.con(0,2,0)"\ 6false\ 5/a\ 6] → P (b1 \ 5a title="boolean and" href="cic:/fakeuri.def(1)"\ 6∧\ 5/a\ 6 b2).
 #b1 #b2 #P (elim b1) normalize // qed.
 
+\ 5img class="anchor" src="icons/tick.png" id="true_to_andb_true"\ 6theorem true_to_andb_true: ∀b1,b2. b1 \ 5a title="leibnitz's equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 6 \ 5a href="cic:/matita/basics/bool/bool.con(0,1,0)"\ 6true\ 5/a\ 6 → b2 \ 5a title="leibnitz's equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 6 \ 5a href="cic:/matita/basics/bool/bool.con(0,1,0)"\ 6true\ 5/a\ 6 → (b1 \ 5a title="boolean and" href="cic:/fakeuri.def(1)"\ 6∧\ 5/a\ 6 b2) \ 5a title="leibnitz's equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 6 \ 5a href="cic:/matita/basics/bool/bool.con(0,1,0)"\ 6true\ 5/a\ 6.
+#b1 cases b1 normalize //
+qed.
+
 \ 5img class="anchor" src="icons/tick.png" id="andb_true_l"\ 6theorem andb_true_l: ∀ b1,b2. (b1 \ 5a title="boolean and" href="cic:/fakeuri.def(1)"\ 6∧\ 5/a\ 6 b2) \ 5a title="leibnitz's equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 6 \ 5a href="cic:/matita/basics/bool/bool.con(0,1,0)"\ 6true\ 5/a\ 6 → b1 \ 5a title="leibnitz's equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 6 \ 5a href="cic:/matita/basics/bool/bool.con(0,1,0)"\ 6true\ 5/a\ 6.
 #b1 (cases b1) normalize // qed.
 
@@ -102,4 +105,4 @@ notation < "hvbox('if' \nbsp term 46 e \nbsp break 'then' \nbsp term 46 t \nbsp
 
 \ 5img class="anchor" src="icons/tick.png" id="true_or_false"\ 6theorem true_or_false:
 ∀b:\ 5a href="cic:/matita/basics/bool/bool.ind(1,0,0)"\ 6bool\ 5/a\ 6. b \ 5a title="leibnitz's equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 6 \ 5a href="cic:/matita/basics/bool/bool.con(0,1,0)"\ 6true\ 5/a\ 6 \ 5a title="logical or" href="cic:/fakeuri.def(1)"\ 6∨\ 5/a\ 6 b \ 5a title="leibnitz's equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 6 \ 5a href="cic:/matita/basics/bool/bool.con(0,2,0)"\ 6false\ 5/a\ 6.
-#b (cases b) /\ 5span class="autotactic"\ 62\ 5span class="autotrace"\ 6 trace \ 5a href="cic:/matita/basics/logic/Or.con(0,1,2)"\ 6or_introl\ 5/a\ 6, \ 5a href="cic:/matita/basics/logic/Or.con(0,2,2)"\ 6or_intror\ 5/a\ 6\ 5/span\ 6\ 5/span\ 6/ qed.
+#b (cases b) /\ 5span class="autotactic"\ 62\ 5span class="autotrace"\ 6 trace \ 5a href="cic:/matita/basics/logic/Or.con(0,1,2)"\ 6or_introl\ 5/a\ 6, \ 5a href="cic:/matita/basics/logic/Or.con(0,2,2)"\ 6or_intror\ 5/a\ 6\ 5/span\ 6\ 5/span\ 6/ qed.
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