Nuprl Lemma : pv11_p1_headers-property
∀[Cmd:ValueAllType]
∀f:pv11_p1_headers_type{i:l}(Cmd)
(((f ``pv11_p1 p1a``) = (Id × pv11_p1_Ballot_Num()) ∈ Type)
∧ ((f ``pv11_p1 p1b``)
= (Id × pv11_p1_Ballot_Num() × pv11_p1_Ballot_Num() × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List))
∈ Type)
∧ ((f ``pv11_p1 p2a``) = (Id × pv11_p1_Ballot_Num() × ℤ × Cmd) ∈ Type)
∧ ((f ``pv11_p1 p2b``) = (Id × pv11_p1_Ballot_Num() × ℤ × pv11_p1_Ballot_Num()) ∈ Type)
∧ ((f ``pv11_p1 preempted``) = pv11_p1_Ballot_Num() ∈ Type)
∧ ((f ``pv11_p1 adopted``) = (pv11_p1_Ballot_Num() × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List)) ∈ Type)
∧ ((f [propose]) = (ℤ × Cmd) ∈ Type)
∧ ((f [decision]) = (ℤ × Cmd) ∈ Type))
Proof
Definitions occuring in Statement :
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Id: Id,
cons: [a / b],
nil: [],
list: T List,
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
and: P ∧ Q,
apply: f a,
product: x:A × B[x],
int: ℤ,
token: "$token",
universe: Type,
equal: s = t ∈ T
Lemmas :
l_all_iff,
name_wf,
pv11_p1_headers_wf,
l_member_wf,
equal_wf,
pv11_p1_headers_fun_wf,
cons_wf_listp,
cons_wf,
nil_wf,
listp_wf,
cons_member,
Id_wf,
pv11_p1_Ballot_Num_wf,
iff_weakening_equal,
equal-wf-base,
list_wf,
pv11_p1_headers_type_wf,
vatype_wf
Latex:
\mforall{}[Cmd:ValueAllType]
\mforall{}f:pv11\_p1\_headers\_type\{i:l\}(Cmd)
(((f ``pv11\_p1 p1a``) = (Id \mtimes{} pv11\_p1\_Ballot\_Num()))
\mwedge{} ((f ``pv11\_p1 p1b``)
= (Id
\mtimes{} pv11\_p1\_Ballot\_Num()
\mtimes{} pv11\_p1\_Ballot\_Num()
\mtimes{} ((pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List)))
\mwedge{} ((f ``pv11\_p1 p2a``) = (Id \mtimes{} pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd))
\mwedge{} ((f ``pv11\_p1 p2b``) = (Id \mtimes{} pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} pv11\_p1\_Ballot\_Num()))
\mwedge{} ((f ``pv11\_p1 preempted``) = pv11\_p1\_Ballot\_Num())
\mwedge{} ((f ``pv11\_p1 adopted``) = (pv11\_p1\_Ballot\_Num() \mtimes{} ((pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List)))
\mwedge{} ((f [propose]) = (\mBbbZ{} \mtimes{} Cmd))
\mwedge{} ((f [decision]) = (\mBbbZ{} \mtimes{} Cmd)))
Date html generated:
2015_07_23-PM-04_43_37
Last ObjectModification:
2015_02_04-AM-07_19_35
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