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
Definitions unfolded in proof :
vatype: ValueAllType,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
rev_implies: P ⇐ Q,
pv11_p1_update_proposals: pv11_p1_update_proposals(Cmd),
so_lambda: λ2x.t[x],
pi1: fst(t),
so_apply: x[s],
or: P ∨ Q,
guard: {T},
cand: A c∧ B,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
not: ¬A,
exists: ∃x:A. B[x],
sq_type: SQType(T),
false: False
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:
2016_05_17-PM-03_17_19
Last ObjectModification:
2015_12_29-PM-11_20_33
Theory : paxos!synod
Home
Index