Nuprl Lemma : assert-rcvset
∀a,b:Id. ∀S:Id List. ∀k:Knd.
(↑rcvset(a;b;S;k) ⇐⇒ ∃i,j:Id. ((i ∈ S) ∧ (j ∈ S) ∧ (k = rcv((link(a) from i to j),b) ∈ Knd)))
Proof
Definitions occuring in Statement :
rcvset: rcvset(a;b;S;k),
rcv: rcv(l,tg),
Knd: Knd,
mk_lnk: (link(n) from i to j),
Id: Id,
l_member: (x ∈ l),
list: T List,
assert: ↑b,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
equal: s = t ∈ T
Lemmas :
assert_wf,
rcvset_wf,
exists_wf,
Id_wf,
l_member_wf,
Knd_wf,
rcv_wf,
mk_lnk_wf,
list_wf,
eq_id_wf,
bool_wf,
eqtt_to_assert,
assert-eq-id,
deq-member_wf,
id-deq_wf,
assert-deq-member,
iff_transitivity,
iff_weakening_uiff,
assert_of_band,
and_wf,
equal_wf,
subtype_base_sq,
atom2_subtype_base,
union_subtype_base,
IdLnk_wf,
product_subtype_base,
isrcv_rcv_lemma,
tag_rcv_lemma,
lnk_rcv_lemma,
lname_mk_lnk_lemma,
lsrc_mk_lnk_lemma,
ldst_mk_lnk_lemma,
member_wf
\mforall{}a,b:Id. \mforall{}S:Id List. \mforall{}k:Knd.
(\muparrow{}rcvset(a;b;S;k) \mLeftarrow{}{}\mRightarrow{} \mexists{}i,j:Id. ((i \mmember{} S) \mwedge{} (j \mmember{} S) \mwedge{} (k = rcv((link(a) from i to j),b))))
Date html generated:
2015_07_17-AM-09_13_19
Last ObjectModification:
2015_01_28-AM-07_57_28
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