Nuprl Lemma : member-links-from-to
∀tg:Id. ∀srclocs,dstlocs:Id List. ∀l:IdLnk.
((l ∈ links(tg) from srclocs to dstlocs)
⇐⇒ {(source(l) ∈ srclocs) ∧ (destination(l) ∈ dstlocs) ∧ (lname(l) = tg ∈ Id)})
Proof
Definitions occuring in Statement :
links-from-to: links(tg) from srclocs to dstlocs,
lname: lname(l),
ldst: destination(l),
lsrc: source(l),
IdLnk: IdLnk,
Id: Id,
l_member: (x ∈ l),
list: T List,
guard: {T},
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
equal: s = t ∈ T
Lemmas :
IdLnk_wf,
list_wf,
Id_wf,
exists_wf,
l_member_wf,
map_wf,
mk_lnk_wf,
lsrc_wf,
ldst_wf,
lname_wf,
member-concat,
member_map,
concat_wf,
iff_wf,
subtype_base_sq,
list_subtype_base,
product_subtype_base,
atom2_subtype_base,
lsrc_mk_lnk_lemma,
ldst_mk_lnk_lemma,
lname_mk_lnk_lemma,
squash_wf,
true_wf
\mforall{}tg:Id. \mforall{}srclocs,dstlocs:Id List. \mforall{}l:IdLnk.
((l \mmember{} links(tg) from srclocs to dstlocs)
\mLeftarrow{}{}\mRightarrow{} \{(source(l) \mmember{} srclocs) \mwedge{} (destination(l) \mmember{} dstlocs) \mwedge{} (lname(l) = tg)\})
Date html generated:
2015_07_17-AM-09_12_20
Last ObjectModification:
2015_01_28-AM-07_57_47
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