Nuprl Lemma : CLK_strict_inc2
∀MsgType:ValueAllType. ∀f:CLK_headers_type{i:l}(MsgType). ∀es:EO+(Message(f)). ∀e1,e2:E. ∀clock1,clock2:ℤ.
((∃e:E. ((e1 <loc e) ∧ e ≤loc e2 ∧ (↑e ∈b CLK_msg'base(MsgType;f))))
⇒ (e1 <loc e2)
⇒ clock1 ∈ CLK_Clock(MsgType;f)(e1)
⇒ clock2 ∈ CLK_Clock(MsgType;f)(e2)
⇒ clock1 < clock2)
Proof
Definitions occuring in Statement :
CLK_Clock: CLK_Clock(MsgType;f),
CLK_msg'base: CLK_msg'base(MsgType;f),
CLK_headers_type: CLK_headers_type{i:l}(MsgType),
Message: Message(f),
classrel: v ∈ X(e),
member-eclass: e ∈b X,
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-E: E,
vatype: ValueAllType,
assert: ↑b,
less_than: a < b,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
int: ℤ
Lemmas :
assert-member-eclass,
CLK_stric_inc,
es-locl_wf,
es-le_wf,
classrel_wf,
exists_wf,
Message_wf,
subtype_rel_dep_function,
name_wf,
vatype_wf,
CLK_Clock_wf,
event-ordering+_subtype,
es-E_wf,
assert_wf,
member-eclass_wf,
CLK_msg'base_wf,
event-ordering+_wf,
CLK_headers_type_wf
Latex:
\mforall{}MsgType:ValueAllType. \mforall{}f:CLK\_headers\_type\{i:l\}(MsgType). \mforall{}es:EO+(Message(f)). \mforall{}e1,e2:E.
\mforall{}clock1,clock2:\mBbbZ{}.
((\mexists{}e:E. ((e1 <loc e) \mwedge{} e \mleq{}loc e2 \mwedge{} (\muparrow{}e \mmember{}\msubb{} CLK\_msg'base(MsgType;f))))
{}\mRightarrow{} (e1 <loc e2)
{}\mRightarrow{} clock1 \mmember{} CLK\_Clock(MsgType;f)(e1)
{}\mRightarrow{} clock2 \mmember{} CLK\_Clock(MsgType;f)(e2)
{}\mRightarrow{} clock1 < clock2)
Date html generated:
2015_07_23-PM-04_10_24
Last ObjectModification:
2015_02_04-PM-02_01_30
Home
Index