Nuprl Lemma : lconnects-transitive
∀p,q:IdLnk List. ∀i,j,k:Id. (∃r:IdLnk List. lconnects(r;i;k)) supposing (lconnects(q;j;k) and lconnects(p;i;j))
Proof
Definitions occuring in Statement :
lconnects: lconnects(p;i;j),
IdLnk: IdLnk,
Id: Id,
list: T List,
uimplies: b supposing a,
all: ∀x:A. B[x],
exists: ∃x:A. B[x]
Lemmas :
IdLnk_wf,
select_wf,
nil_wf,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
add-associates,
add-swap,
add-commutes,
sq_stable__le,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
decidable__lt,
length_wf,
less-iff-le,
subtract_wf,
lnk-inv_wf,
le-add-cancel2,
int_seg_wf,
equal-wf-base,
not_wf,
equal-wf-T-base,
lconnects_wf,
squash_wf,
true_wf,
length_of_nil_lemma,
Id_wf,
list_wf,
cons_wf,
length_of_cons_lemma,
reduce_hd_cons_lemma,
non_neg_length,
length_wf_nat,
ldst_wf,
lpath_cons,
list-cases,
product_subtype_list,
last_cons,
assert_elim,
null_wf3,
subtype_rel_list,
top_wf,
null_cons_lemma,
bfalse_wf,
btrue_neq_bfalse,
assert_wf,
iff_weakening_equal,
less_than_wf,
last_wf,
last_singleton,
less_than_transitivity1,
less_than_irreflexivity,
decidable__equal_IdLnk,
subtype_base_sq,
product_subtype_base,
atom2_subtype_base,
ldst-inv,
length_cons,
null_nil_lemma,
iff_weakening_uiff,
lpath_wf,
lsrc_wf,
hd_wf,
equal_wf
\mforall{}p,q:IdLnk List. \mforall{}i,j,k:Id.
(\mexists{}r:IdLnk List. lconnects(r;i;k)) supposing (lconnects(q;j;k) and lconnects(p;i;j))
Date html generated:
2015_07_17-AM-09_13_12
Last ObjectModification:
2015_02_04-PM-05_08_43
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