Nuprl Lemma : CLK_stric_inc
∀MsgType:ValueAllType. ∀f:CLK_headers_type{i:l}(MsgType). ∀es:EO+(Message(f)). ∀e1,e2:E. ∀clock1,clock2:ℤ.
((∃a:MsgType × ℤ. ∃e:E. ((e1 <loc e) ∧ e ≤loc e2 ∧ a ∈ CLK_msg'base(MsgType;f)(e)))
⇒ (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),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-E: E,
vatype: ValueAllType,
less_than: a < b,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
product: x:A × B[x],
int: ℤ
Lemmas :
int_seg_wf,
length_wf,
name_wf,
CLK_headers_wf,
l_all_iff,
l_member_wf,
equal_wf,
CLK_headers_fun_wf,
cons_wf_listp,
cons_wf,
nil_wf,
listp_wf,
cons_member,
iff_weakening_equal,
classrel_wf,
squash_wf,
true_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf,
State1-state-class1,
CLK_upd_clock_wf,
Id_wf,
CLK_msg'base_wf,
State-loc-comb-trans1,
less_than_wf,
single-bag_wf,
less_than_transitivity2,
le_weakening2,
State-loc-comb_wf,
es-pred_wf,
assert_elim,
es-first_wf2,
es-locl-first,
btrue_neq_bfalse,
assert_wf,
es-le_wf,
es-locl_wf,
base-headers-msg-val-single-val,
subtype_rel_weakening,
ext-eq_weakening,
single-valued-bag-single,
exists_wf,
member-less_than,
CLK_Clock_wf,
Message_wf,
subtype_rel_dep_function,
vatype_wf,
CLK_headers_type_wf,
set_wf,
valueall-type_wf,
value-type-has-value,
int-value-type,
le_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_le_int,
decidable__lt,
false_wf,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
add-mul-special,
zero-mul,
add-zero,
add-associates,
add-commutes,
le-add-cancel,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
le_wf,
not-le-2,
add_functionality_wrt_le
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{}a:MsgType \mtimes{} \mBbbZ{}. \mexists{}e:E. ((e1 <loc e) \mwedge{} e \mleq{}loc e2 \mwedge{} a \mmember{} CLK\_msg'base(MsgType;f)(e)))
{}\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_09_57
Last ObjectModification:
2015_04_08-AM-10_50_50
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