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why3/examples/numeric/substraction/why3session.xml
Matteo Manighetti 7ae65be566 Upgrade sessions to use Alt-Ergo 2.6.0
2025-01-14 19:48:35 +01:00

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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"https://www.why3.org/why3session.dtd">
<why3session shape_version="6">
<prover id="1" name="Alt-Ergo" version="2.6.0" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="substraction.mlw"/>
<theory name="SubstractionSingle" proved="true">
<goal name="substraction_errors_basic&#39;vc" expl="VC for substraction_errors_basic" proved="true">
<transf name="split_vc" proved="true" >
<goal name="substraction_errors_basic&#39;vc.0" expl="postcondition" proved="true">
<transf name="assert" proved="true" arg1="let t = to_real c in
let t1 = 1.0 +. eps in
let t2 = to_real a -. to_real b in
abs (to_real result -. (t2 -. t))
&lt;=. ((((eps +. 0.0) +. eps) *. (abs t2 +. abs t))
+. (((t1 +. 0.0) *. 0.0) +. ((t1 +. eps) *. 0.0)))">
<goal name="substraction_errors_basic&#39;vc.0.0" expl="asserted formula" proved="true">
<transf name="assert" proved="true" arg1="abs (to_real result -. ((to_real a -. to_real b) -. to_real c))
&lt;=. ((((eps +. 0.0) +. eps)
*. (abs (to_real a -. to_real b) +. abs (to_real c)))
+. ((((1.0 +. eps) +. 0.0) *. 0.0) +. (((1.0 +. eps) +. eps) *. 0.0)))">
<goal name="substraction_errors_basic&#39;vc.0.0.0" expl="asserted formula" proved="true">
<transf name="apply" proved="true" arg1="usub_single_error_propagation" arg2="with" arg3="a --. b,c">
<goal name="substraction_errors_basic&#39;vc.0.0.0.0" expl="apply premises" proved="true">
<transf name="assert" proved="true" arg1="abs (to_real (a --. b) -. (to_real a -. to_real b))
&lt;=. (eps *. abs (to_real a -. to_real b))">
<goal name="substraction_errors_basic&#39;vc.0.0.0.0.0" expl="asserted formula" proved="true">
<proof prover="1"><result status="valid" time="0.039705" steps="723"/></proof>
</goal>
<goal name="substraction_errors_basic&#39;vc.0.0.0.0.1" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.015924" steps="115"/></proof>
</goal>
</transf>
</goal>
<goal name="substraction_errors_basic&#39;vc.0.0.0.1" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.012067" steps="89"/></proof>
</goal>
<goal name="substraction_errors_basic&#39;vc.0.0.0.2" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.017003" steps="92"/></proof>
</goal>
<goal name="substraction_errors_basic&#39;vc.0.0.0.3" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.012202" steps="92"/></proof>
</goal>
<goal name="substraction_errors_basic&#39;vc.0.0.0.4" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.014883" steps="84"/></proof>
</goal>
<goal name="substraction_errors_basic&#39;vc.0.0.0.5" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.013623" steps="84"/></proof>
</goal>
<goal name="substraction_errors_basic&#39;vc.0.0.0.6" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.013115" steps="84"/></proof>
</goal>
<goal name="substraction_errors_basic&#39;vc.0.0.0.7" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.016362" steps="84"/></proof>
</goal>
<goal name="substraction_errors_basic&#39;vc.0.0.0.8" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.013187" steps="83"/></proof>
</goal>
</transf>
</goal>
<goal name="substraction_errors_basic&#39;vc.0.0.1" expl="asserted formula" proved="true">
<proof prover="1"><result status="valid" time="0.028274" steps="198"/></proof>
</goal>
</transf>
</goal>
<goal name="substraction_errors_basic&#39;vc.0.1" expl="postcondition" proved="true">
<proof prover="1"><result status="valid" time="0.041960" steps="371"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
<goal name="substraction_errors&#39;vc" expl="VC for substraction_errors" proved="true">
<transf name="split_vc" proved="true" >
<goal name="substraction_errors&#39;vc.0" expl="postcondition" proved="true">
<transf name="assert" proved="true" arg1="let t = to_real d in
let t1 = to_real c in
let t2 = eps +. eps in
let t3 = to_real e -. to_real f in
let t4 = to_real a -. to_real b in
let t5 = ((1.0 +. eps) +. t2) *. 0.0 in
abs (to_real result -. ((t4 -. t1) -. (t -. t3)))
&lt;=. ((((t2 +. t2) +. eps) *. ((abs t4 +. abs t1) +. (abs t +. abs t3)))
+. (t5 +. t5))">
<goal name="substraction_errors&#39;vc.0.0" expl="asserted formula" proved="true">
<transf name="assert" proved="true" arg1="abs
(to_real result
-. (((to_real a -. to_real b) -. to_real c)
-. (to_real d -. (to_real e -. to_real f))))
&lt;=. (((((eps +. eps) +. (eps +. eps)) +. eps)
*. ((abs (to_real a -. to_real b) +. abs (to_real c))
+. (abs (to_real d) +. abs (to_real e -. to_real f))))
+. ((((1.0 +. eps) +. (eps +. eps)) *. 0.0)
+. (((1.0 +. eps) +. (eps +. eps)) *. 0.0)))">
<goal name="substraction_errors&#39;vc.0.0.0" expl="asserted formula" proved="true">
<transf name="apply" proved="true" arg1="usub_single_error_propagation" arg2="with" arg3="(a --. b) --. c,d --. (e --. f)">
<goal name="substraction_errors&#39;vc.0.0.0.0" expl="apply premises" proved="true">
<transf name="assert" proved="true" arg1="abs (to_real ((a --. b) --. c) -. ((to_real a -. to_real b) -. to_real c))
&lt;=. ((((eps +. 0.0) +. eps)
*. (abs (to_real a -. to_real b) +. abs (to_real c)))
+. ((((1.0 +. eps) +. 0.0) *. 0.0) +. (((1.0 +. eps) +. eps) *. 0.0)))">
<goal name="substraction_errors&#39;vc.0.0.0.0.0" expl="asserted formula" proved="true">
<transf name="apply" proved="true" arg1="usub_single_error_propagation" arg2="with" arg3="a --. b,c">
<goal name="substraction_errors&#39;vc.0.0.0.0.0.0" expl="apply premises" proved="true">
<transf name="assert" proved="true" arg1="abs (to_real (a --. b) -. (to_real a -. to_real b))
&lt;=. (eps *. abs (to_real a -. to_real b))">
<goal name="substraction_errors&#39;vc.0.0.0.0.0.0.0" expl="asserted formula" proved="true">
<proof prover="1"><result status="valid" time="0.039116" steps="723"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.0.0.0.1" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.017451" steps="115"/></proof>
</goal>
</transf>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.0.0.1" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.020543" steps="89"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.0.0.2" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.016043" steps="92"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.0.0.3" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.019725" steps="92"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.0.0.4" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.016456" steps="84"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.0.0.5" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.018428" steps="84"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.0.0.6" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.020320" steps="84"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.0.0.7" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.013344" steps="84"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.0.0.8" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.014676" steps="83"/></proof>
</goal>
</transf>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.0.1" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.020530" steps="144"/></proof>
</goal>
</transf>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.1" expl="apply premises" proved="true">
<transf name="assert" proved="true" arg1="abs (to_real (d --. (e --. f)) -. (to_real d -. (to_real e -. to_real f)))
&lt;=. ((((0.0 +. eps) +. eps)
*. (abs (to_real d) +. abs (to_real e -. to_real f)))
+. ((((1.0 +. eps) +. eps) *. 0.0) +. (((1.0 +. eps) +. 0.0) *. 0.0)))">
<goal name="substraction_errors&#39;vc.0.0.0.1.0" expl="asserted formula" proved="true">
<transf name="apply" proved="true" arg1="usub_single_error_propagation" arg2="with" arg3="d,e --. f">
<goal name="substraction_errors&#39;vc.0.0.0.1.0.0" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.014739" steps="89"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.1.0.1" expl="apply premises" proved="true">
<transf name="assert" proved="true" arg1="abs (to_real (e --. f) -. (to_real e -. to_real f))
&lt;=. (eps *. abs (to_real e -. to_real f))">
<goal name="substraction_errors&#39;vc.0.0.0.1.0.1.0" expl="asserted formula" proved="true">
<proof prover="1"><result status="valid" time="0.041533" steps="723"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.1.0.1.1" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.014262" steps="115"/></proof>
</goal>
</transf>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.1.0.2" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.014873" steps="92"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.1.0.3" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.015998" steps="92"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.1.0.4" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.015247" steps="84"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.1.0.5" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.015105" steps="84"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.1.0.6" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.014480" steps="84"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.1.0.7" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.011594" steps="84"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.1.0.8" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.014263" steps="83"/></proof>
</goal>
</transf>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.1.1" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.018609" steps="152"/></proof>
</goal>
</transf>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.2" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.017101" steps="122"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.3" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.017462" steps="116"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.4" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.018061" steps="84"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.5" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.015492" steps="84"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.6" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.014949" steps="84"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.7" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.014738" steps="84"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.8" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.012286" steps="83"/></proof>
</goal>
</transf>
</goal>
<goal name="substraction_errors&#39;vc.0.0.1" expl="asserted formula" proved="true">
<proof prover="1"><result status="valid" time="0.092121" steps="613"/></proof>
</goal>
</transf>
</goal>
<goal name="substraction_errors&#39;vc.0.1" expl="postcondition" proved="true">
<proof prover="1"><result status="valid" time="0.683527" steps="2765"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
</theory>
<theory name="SubstractionDouble" proved="true">
<goal name="substraction_errors_basic&#39;vc" expl="VC for substraction_errors_basic" proved="true">
<transf name="split_vc" proved="true" >
<goal name="substraction_errors_basic&#39;vc.0" expl="postcondition" proved="true">
<transf name="assert" proved="true" arg1="let t = to_real c in
let t1 = 1.0 +. eps in
let t2 = to_real a -. to_real b in
abs (to_real result -. (t2 -. t))
&lt;=. ((((eps +. 0.0) +. eps) *. (abs t2 +. abs t))
+. (((t1 +. 0.0) *. 0.0) +. ((t1 +. eps) *. 0.0)))">
<goal name="substraction_errors_basic&#39;vc.0.0" expl="asserted formula" proved="true">
<transf name="assert" proved="true" arg1="abs (to_real result -. ((to_real a -. to_real b) -. to_real c))
&lt;=. ((((eps +. 0.0) +. eps)
*. (abs (to_real a -. to_real b) +. abs (to_real c)))
+. ((((1.0 +. eps) +. 0.0) *. 0.0) +. (((1.0 +. eps) +. eps) *. 0.0)))">
<goal name="substraction_errors_basic&#39;vc.0.0.0" expl="asserted formula" proved="true">
<transf name="apply" proved="true" arg1="usub_double_error_propagation" arg2="with" arg3="a --. b,c">
<goal name="substraction_errors_basic&#39;vc.0.0.0.0" expl="apply premises" proved="true">
<transf name="assert" proved="true" arg1="abs (to_real (a --. b) -. (to_real a -. to_real b))
&lt;=. (eps *. abs (to_real a -. to_real b))">
<goal name="substraction_errors_basic&#39;vc.0.0.0.0.0" expl="asserted formula" proved="true">
<proof prover="1"><result status="valid" time="0.040899" steps="723"/></proof>
</goal>
<goal name="substraction_errors_basic&#39;vc.0.0.0.0.1" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.017314" steps="115"/></proof>
</goal>
</transf>
</goal>
<goal name="substraction_errors_basic&#39;vc.0.0.0.1" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.017142" steps="89"/></proof>
</goal>
<goal name="substraction_errors_basic&#39;vc.0.0.0.2" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.012805" steps="92"/></proof>
</goal>
<goal name="substraction_errors_basic&#39;vc.0.0.0.3" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.018154" steps="92"/></proof>
</goal>
<goal name="substraction_errors_basic&#39;vc.0.0.0.4" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.014130" steps="84"/></proof>
</goal>
<goal name="substraction_errors_basic&#39;vc.0.0.0.5" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.018020" steps="84"/></proof>
</goal>
<goal name="substraction_errors_basic&#39;vc.0.0.0.6" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.015565" steps="84"/></proof>
</goal>
<goal name="substraction_errors_basic&#39;vc.0.0.0.7" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.015286" steps="84"/></proof>
</goal>
<goal name="substraction_errors_basic&#39;vc.0.0.0.8" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.014466" steps="83"/></proof>
</goal>
</transf>
</goal>
<goal name="substraction_errors_basic&#39;vc.0.0.1" expl="asserted formula" proved="true">
<proof prover="1"><result status="valid" time="0.024136" steps="198"/></proof>
</goal>
</transf>
</goal>
<goal name="substraction_errors_basic&#39;vc.0.1" expl="postcondition" proved="true">
<proof prover="1"><result status="valid" time="0.048284" steps="371"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
<goal name="substraction_errors&#39;vc" expl="VC for substraction_errors" proved="true">
<transf name="split_vc" proved="true" >
<goal name="substraction_errors&#39;vc.0" expl="postcondition" proved="true">
<transf name="assert" proved="true" arg1="let t = to_real d in
let t1 = to_real c in
let t2 = eps +. eps in
let t3 = to_real e -. to_real f in
let t4 = to_real a -. to_real b in
let t5 = ((1.0 +. eps) +. t2) *. 0.0 in
abs (to_real result -. ((t4 -. t1) -. (t -. t3)))
&lt;=. ((((t2 +. t2) +. eps) *. ((abs t4 +. abs t1) +. (abs t +. abs t3)))
+. (t5 +. t5))">
<goal name="substraction_errors&#39;vc.0.0" expl="asserted formula" proved="true">
<transf name="assert" proved="true" arg1="abs
(to_real result
-. (((to_real a -. to_real b) -. to_real c)
-. (to_real d -. (to_real e -. to_real f))))
&lt;=. (((((eps +. eps) +. (eps +. eps)) +. eps)
*. ((abs (to_real a -. to_real b) +. abs (to_real c))
+. (abs (to_real d) +. abs (to_real e -. to_real f))))
+. ((((1.0 +. eps) +. (eps +. eps)) *. 0.0)
+. (((1.0 +. eps) +. (eps +. eps)) *. 0.0)))">
<goal name="substraction_errors&#39;vc.0.0.0" expl="asserted formula" proved="true">
<transf name="apply" proved="true" arg1="usub_double_error_propagation" arg2="with" arg3="(a --. b) --. c,d --. (e --. f)">
<goal name="substraction_errors&#39;vc.0.0.0.0" expl="apply premises" proved="true">
<transf name="assert" proved="true" arg1="abs (to_real ((a --. b) --. c) -. ((to_real a -. to_real b) -. to_real c))
&lt;=. ((((eps +. 0.0) +. eps)
*. (abs (to_real a -. to_real b) +. abs (to_real c)))
+. ((((1.0 +. eps) +. 0.0) *. 0.0) +. (((1.0 +. eps) +. eps) *. 0.0)))">
<goal name="substraction_errors&#39;vc.0.0.0.0.0" expl="asserted formula" proved="true">
<transf name="apply" proved="true" arg1="usub_double_error_propagation" arg2="with" arg3="a --. b,c">
<goal name="substraction_errors&#39;vc.0.0.0.0.0.0" expl="apply premises" proved="true">
<transf name="assert" proved="true" arg1="abs (to_real (a --. b) -. (to_real a -. to_real b))
&lt;=. (eps *. abs (to_real a -. to_real b))">
<goal name="substraction_errors&#39;vc.0.0.0.0.0.0.0" expl="asserted formula" proved="true">
<proof prover="1"><result status="valid" time="0.044775" steps="723"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.0.0.0.1" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.020180" steps="115"/></proof>
</goal>
</transf>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.0.0.1" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.021562" steps="89"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.0.0.2" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.017258" steps="92"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.0.0.3" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.015673" steps="92"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.0.0.4" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.017849" steps="84"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.0.0.5" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.017039" steps="84"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.0.0.6" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.019294" steps="84"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.0.0.7" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.016156" steps="84"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.0.0.8" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.019100" steps="83"/></proof>
</goal>
</transf>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.0.1" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.020572" steps="144"/></proof>
</goal>
</transf>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.1" expl="apply premises" proved="true">
<transf name="assert" proved="true" arg1="abs (to_real (d --. (e --. f)) -. (to_real d -. (to_real e -. to_real f)))
&lt;=. ((((0.0 +. eps) +. eps)
*. (abs (to_real d) +. abs (to_real e -. to_real f)))
+. ((((1.0 +. eps) +. eps) *. 0.0) +. (((1.0 +. eps) +. 0.0) *. 0.0)))">
<goal name="substraction_errors&#39;vc.0.0.0.1.0" expl="asserted formula" proved="true">
<transf name="apply" proved="true" arg1="usub_double_error_propagation" arg2="with" arg3="d,e --. f">
<goal name="substraction_errors&#39;vc.0.0.0.1.0.0" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.014144" steps="89"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.1.0.1" expl="apply premises" proved="true">
<transf name="assert" proved="true" arg1="abs (to_real (e --. f) -. (to_real e -. to_real f))
&lt;=. (eps *. abs (to_real e -. to_real f))">
<goal name="substraction_errors&#39;vc.0.0.0.1.0.1.0" expl="asserted formula" proved="true">
<proof prover="1"><result status="valid" time="0.042873" steps="723"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.1.0.1.1" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.020348" steps="115"/></proof>
</goal>
</transf>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.1.0.2" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.015125" steps="92"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.1.0.3" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.014370" steps="92"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.1.0.4" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.014733" steps="84"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.1.0.5" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.016034" steps="84"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.1.0.6" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.011815" steps="84"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.1.0.7" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.017854" steps="84"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.1.0.8" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.015277" steps="83"/></proof>
</goal>
</transf>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.1.1" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.022236" steps="152"/></proof>
</goal>
</transf>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.2" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.017706" steps="122"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.3" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.014809" steps="116"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.4" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.013262" steps="84"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.5" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.016992" steps="84"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.6" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.015925" steps="84"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.7" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.014043" steps="84"/></proof>
</goal>
<goal name="substraction_errors&#39;vc.0.0.0.8" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.016216" steps="83"/></proof>
</goal>
</transf>
</goal>
<goal name="substraction_errors&#39;vc.0.0.1" expl="asserted formula" proved="true">
<proof prover="1"><result status="valid" time="0.084850" steps="613"/></proof>
</goal>
</transf>
</goal>
<goal name="substraction_errors&#39;vc.0.1" expl="postcondition" proved="true">
<proof prover="1"><result status="valid" time="0.658332" steps="2759"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
</theory>
</file>
</why3session>
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