Nuprl Lemma : pv11_p1_upd_desc_iff
∀Cmd:ValueAllType. ∀proposals1,proposals2:(ℤ × Cmd) List. ∀s:ℤ. ∀c:Cmd.
((<s, c> ∈ pv11_p1_update_proposals(Cmd) proposals1 proposals2)
⇐⇒ (<s, c> ∈ proposals2) ∨ ((<s, c> ∈ proposals1) ∧ (¬(∃c':Cmd. (<s, c'> ∈ proposals2)))))
Proof
Definitions occuring in Statement :
pv11_p1_update_proposals: pv11_p1_update_proposals(Cmd),
l_member: (x ∈ l),
list: T List,
vatype: ValueAllType,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
or: P ∨ Q,
and: P ∧ Q,
apply: f a,
pair: <a, b>,
product: x:A × B[x],
int: ℤ
Lemmas :
pv11_p1_upd_desc,
l_member_wf,
pv11_p1_update_proposals_wf,
member_append,
filter_wf5,
bnot_wf,
bl-exists_wf,
eq_int_wf,
member_filter_2,
iff_transitivity,
assert_wf,
not_wf,
l_exists_wf,
equal-wf-base-T,
int_subtype_base,
iff_weakening_uiff,
assert_of_bnot,
l_exists_functionality,
assert_of_eq_int,
set_wf,
assert-bl-exists,
l_exists_iff,
subtype_base_sq,
pair-eta,
or_wf,
exists_wf,
list_wf,
valueall-type_wf
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}proposals1,proposals2:(\mBbbZ{} \mtimes{} Cmd) List. \mforall{}s:\mBbbZ{}. \mforall{}c:Cmd.
((<s, c> \mmember{} pv11\_p1\_update\_proposals(Cmd) proposals1 proposals2)
\mLeftarrow{}{}\mRightarrow{} (<s, c> \mmember{} proposals2) \mvee{} ((<s, c> \mmember{} proposals1) \mwedge{} (\mneg{}(\mexists{}c':Cmd. (<s, c'> \mmember{} proposals2)))))
Date html generated:
2015_07_23-PM-04_44_54
Last ObjectModification:
2015_01_29-AM-09_53_36
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