At:
dfs-measure
For any graph
the_obj:GraphObject(the_graph).
M:(Traversal

). (
i:V, s:Traversal. M([inl(i) / s])
M(s)) & (
i:V, s:Traversal.
member-paren(x,y.the_obj.eq(x,y);i;s) 
M([inr(i) / s]) < M(s))
By:
RepeatFor 2 (Analyze 0)
THEN
Inst
Thm* graphobj-properties
[the_graph;the_obj]
THEN
Analyze -1
THEN
Analyze -1
THEN
InstConcl [
s.vertex-count(the_obj;i.
member-right-paren(x,y.the_obj.eq(x,y);i;s))]
THEN
Reduce 0
THEN
Try
(BackThru
Thm* For any graph
the_obj:GraphObject(the_graph), P,Q:(V

). (
x:V. P(x) 
Q(x)) 
vertex-count(the_obj;x.P(x))
vertex-count(the_obj;x.Q(x)))
THEN
Try
(BackThru
Thm* For any graph
the_obj:GraphObject(the_graph), P,Q:(V

). (
x:V. P(x) 
Q(x)) 
(
x:V.
P(x) & Q(x)) 
vertex-count(the_obj;x.P(x)) < vertex-count(the_obj;x.Q(x)))
THEN
RW assert_pushdownC 0
THEN
RW assert_pushdownC -1
THEN
RWO
Thm*
E:(T
T

). (
x,y:T. E(x,y) 
x = y) 
(
i:T, s:(T+T) List. member-right-paren(x,y.E(x,y);i;s) 
(inr(i)
s))
0
THEN
Try
(RWO
Thm*
E:(T
T

). (
x,y:T. E(x,y) 
x = y) 
(
i:T, s:(T+T) List. member-right-paren(x,y.E(x,y);i;s) 
(inr(i)
s))
-1)
THEN
Try
(RWO
Thm*
E:(T
T

). (
x,y:T. E(x,y) 
x = y) 
(
i:T, s:(T+T) List. member-paren(x,y.E(x,y);i;s) 
(inl(i)
s)
(inr(i)
s))
-1)
THEN
Try (InstConcl [i])
THEN
ObviousFrom [-1]
Generated subgoals:
None
About: