Nuprl Lemma : new_23_sig_rounds_mem_fun
∀Cmd:ValueAllType. ∀notify,propose:Atom List. ∀f:new_23_sig_headers_type{i:l}(Cmd;notify;propose). ∀es:EO+(Message(f)).
∀e1,e2:E. ∀n,round:ℤ. ∀cmd:Cmd.
((e1 <loc e2)
⇒ <<n, round>, cmd> ∈ new_23_sig_RoundInfo(Cmd;notify;propose;f)(e1)
⇒ (round ≤ new_23_sig_NewRoundsStateFun(Cmd;notify;propose;f;n;es;e2)))
Proof
Definitions occuring in Statement :
new_23_sig_NewRoundsStateFun: new_23_sig_NewRoundsStateFun(Cmd;notify;propose;f;x;es;e),
new_23_sig_RoundInfo: new_23_sig_RoundInfo(Cmd;notify;propose;f),
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose),
Message: Message(f),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
list: T List,
vatype: ValueAllType,
le: A ≤ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
pair: <a, b>,
product: x:A × B[x],
int: ℤ,
atom: Atom
Definitions unfolded in proof :
vatype: ValueAllType,
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s]
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}notify,propose:Atom List. \mforall{}f:new\_23\_sig\_headers\_type\{i:l\}(Cmd;notify;propose).
\mforall{}es:EO+(Message(f)). \mforall{}e1,e2:E. \mforall{}n,round:\mBbbZ{}. \mforall{}cmd:Cmd.
((e1 <loc e2)
{}\mRightarrow{} <<n, round>, cmd> \mmember{} new\_23\_sig\_RoundInfo(Cmd;notify;propose;f)(e1)
{}\mRightarrow{} (round \mleq{} new\_23\_sig\_NewRoundsStateFun(Cmd;notify;propose;f;n;es;e2)))
Date html generated:
2016_05_17-PM-02_14_55
Last ObjectModification:
2016_01_18-AM-09_32_18
Theory : 2!3!consensus!with!signatures
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