Commit c3af2d13 authored by MARCHE Claude's avatar MARCHE Claude
Browse files

bitvector/power2: missing proofs added

parent 29df0abf
......@@ -83,32 +83,9 @@ theory Pow2int
use import int.EuclideanDivision
(*
lemma div_uniq:
forall x y q:int.
y > 0 /\ (exists r:int. x = q*y + r /\ 0 <= r < y) -> div x y = q
lemma mod_uniq:
forall x y r:int.
y > 0 /\ (exists q:int. x = q*y + r /\ 0 <= r < y) -> mod x y = r
lemma Div_double_aux:
forall x y:int. 0 < y <= x < 2*y ->
x = 1*y+(x-y) /\ 0 <= x-y < y
lemma Div_double_aux2:
forall x y:int. 0 < y <= x < 2*y -> mod x y = x - y
*)
(*
lemma Div_mult :
forall x y q:int. q > 0 ->
0 < q*y <= x < (q+1)*y -> div x y = q
lemma Div_mult_neg :
forall x y q:int. q > 0 ->
-(q+1)*y <= x < -q*y < 0 -> div x y = -(q+1)
*)
lemma Div_mult_inst: forall x z:int.
x > 0 ->
div (x * 1 + z) x = 1 + div z x
lemma Div_double:
forall x y:int. 0 < y <= x < 2*y -> div x y = 1
......
......@@ -15,18 +15,22 @@
version="2.4.1"/>
<prover
id="3"
name="CVC4"
version="1.0"/>
<prover
id="4"
name="Coq"
version="8.4pl2"/>
<prover
id="4"
id="5"
name="Gappa"
version="1.0.0"/>
<prover
id="5"
id="6"
name="Z3"
version="2.19"/>
<prover
id="6"
id="7"
name="Z3"
version="3.2"/>
<file
......@@ -72,7 +76,7 @@
<result status="valid" time="0.00"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -80,7 +84,7 @@
<result status="valid" time="0.00"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -97,7 +101,7 @@
expanded="false"
shape="ainfix =apow2ainfix +V0V1ainfix *apow2V0apow2V1Iainfix &gt;=V1c0Aainfix &gt;=V0c0F">
<proof
prover="3"
prover="4"
timelimit="5"
memlimit="1000"
edited="power2_Pow2int_Power_sum_1.v"
......@@ -115,7 +119,7 @@
expanded="false"
shape="ainfix &gt;apow2V0c0Iainfix &gt;=V0c0F">
<proof
prover="3"
prover="4"
timelimit="5"
memlimit="1000"
edited="power2_Pow2int_pow2pos_1.v"
......@@ -157,7 +161,7 @@
<result status="valid" time="0.00"/>
</proof>
<proof
prover="4"
prover="5"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -165,7 +169,7 @@
<result status="valid" time="0.00"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -173,7 +177,7 @@
<result status="valid" time="0.00"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -214,7 +218,7 @@
<result status="valid" time="0.00"/>
</proof>
<proof
prover="4"
prover="5"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -222,7 +226,7 @@
<result status="valid" time="0.00"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -230,7 +234,7 @@
<result status="valid" time="0.00"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -271,7 +275,7 @@
<result status="valid" time="0.01"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -279,7 +283,7 @@
<result status="valid" time="0.00"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -320,7 +324,7 @@
<result status="valid" time="0.00"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -328,7 +332,7 @@
<result status="valid" time="0.00"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -369,7 +373,7 @@
<result status="valid" time="0.01"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -377,7 +381,7 @@
<result status="valid" time="0.01"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -418,7 +422,7 @@
<result status="valid" time="0.00"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -426,7 +430,7 @@
<result status="valid" time="0.02"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -467,7 +471,7 @@
<result status="valid" time="0.00"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -475,7 +479,7 @@
<result status="valid" time="0.02"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -516,7 +520,7 @@
<result status="valid" time="0.00"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -524,7 +528,7 @@
<result status="valid" time="0.01"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -565,7 +569,7 @@
<result status="valid" time="0.00"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -573,7 +577,7 @@
<result status="valid" time="0.02"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -614,7 +618,7 @@
<result status="valid" time="0.00"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -622,7 +626,7 @@
<result status="valid" time="0.04"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -663,7 +667,7 @@
<result status="valid" time="0.02"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -671,7 +675,7 @@
<result status="valid" time="0.02"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -712,7 +716,7 @@
<result status="valid" time="0.00"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -720,7 +724,7 @@
<result status="valid" time="0.05"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -761,7 +765,7 @@
<result status="valid" time="0.01"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -769,7 +773,7 @@
<result status="valid" time="0.02"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -810,7 +814,7 @@
<result status="valid" time="0.00"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -818,7 +822,7 @@
<result status="valid" time="0.02"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -859,7 +863,7 @@
<result status="valid" time="0.02"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -867,7 +871,7 @@
<result status="valid" time="0.09"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -908,7 +912,7 @@
<result status="valid" time="0.00"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -916,7 +920,7 @@
<result status="valid" time="0.10"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -957,7 +961,7 @@
<result status="valid" time="0.01"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -965,7 +969,7 @@
<result status="valid" time="0.04"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1006,7 +1010,7 @@
<result status="valid" time="0.00"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1014,7 +1018,7 @@
<result status="valid" time="0.12"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1055,7 +1059,7 @@
<result status="valid" time="0.01"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1063,7 +1067,7 @@
<result status="valid" time="0.15"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1104,7 +1108,7 @@
<result status="valid" time="0.00"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1112,7 +1116,7 @@
<result status="valid" time="0.04"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1153,7 +1157,7 @@
<result status="valid" time="0.01"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1161,7 +1165,7 @@
<result status="valid" time="0.17"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1202,7 +1206,7 @@
<result status="valid" time="0.00"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1210,7 +1214,7 @@
<result status="valid" time="0.19"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1251,7 +1255,7 @@
<result status="valid" time="0.02"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1259,7 +1263,7 @@
<result status="valid" time="0.05"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1300,7 +1304,7 @@
<result status="valid" time="0.00"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1308,7 +1312,7 @@
<result status="valid" time="0.24"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1349,7 +1353,7 @@
<result status="valid" time="0.02"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1357,7 +1361,7 @@
<result status="valid" time="0.07"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1398,7 +1402,7 @@
<result status="valid" time="0.00"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1406,7 +1410,7 @@
<result status="valid" time="0.29"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1447,7 +1451,7 @@
<result status="valid" time="0.01"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1455,7 +1459,7 @@
<result status="valid" time="0.07"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1496,7 +1500,7 @@
<result status="valid" time="0.00"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1504,7 +1508,7 @@
<result status="valid" time="0.36"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1545,7 +1549,7 @@
<result status="valid" time="0.02"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1553,7 +1557,7 @@
<result status="valid" time="0.08"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1594,7 +1598,7 @@
<result status="valid" time="0.01"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1602,7 +1606,7 @@
<result status="valid" time="0.09"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1643,7 +1647,7 @@
<result status="valid" time="0.02"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1651,7 +1655,7 @@
<result status="valid" time="0.09"/>
</proof>
<proof
prover="6"
prover="7"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1692,7 +1696,7 @@
<result status="valid" time="0.00"/>
</proof>
<proof
prover="5"
prover="6"
timelimit="5"
memlimit="1000"
obsolete="false"
......@@ -1700,7 +1704,7 @@
<result status="valid" time="0.47"/>
</proof>
<proof
prover="6"