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
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
and: P ∧ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
vatype: ValueAllType,
iff: P ⇐⇒ Q,
squash: ↓T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
CLK_headers_type: CLK_headers_type{i:l}(MsgType),
subtype_rel: A ⊆r B,
uimplies: b supposing a
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:
2016_05_17-PM-02_46_02
Last ObjectModification:
2015_12_29-PM-10_18_56
Theory : lamport!s!clocks
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