PrintForm Definitions Lemmas graph 1 3 Sections Graphs Doc

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:(TT). (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:(TT). (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:(TT). (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:
listconsboolassertless_thanunioninlinrlambdaapply
functionuniverseequalimpliesandorall
exists

PrintForm Definitions Lemmas graph 1 3 Sections Graphs Doc