Nuprl Lemma : run_local_pred_time_less
∀M:Type ⟶ Type. ∀r:pRunType(P.M[P]). ∀e,x:runEvents(r).
  ((run-event-loc(x) = run-event-loc(e) ∈ Id)
  
⇒ run-event-step(x) < run-event-step(e)
  
⇒ run-event-step(run_local_pred(r;e)) < run-event-step(e))
Proof
Definitions occuring in Statement : 
run_local_pred: run_local_pred(r;e)
, 
run-event-step: run-event-step(e)
, 
run-event-loc: run-event-loc(e)
, 
runEvents: runEvents(r)
, 
pRunType: pRunType(T.M[T])
, 
Id: Id
, 
less_than: a < b
, 
so_apply: x[s]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
function: x:A ⟶ B[x]
, 
universe: Type
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
runEvents: runEvents(r)
, 
run-event-step: run-event-step(e)
, 
run-event-loc: run-event-loc(e)
, 
pi2: snd(t)
, 
pi1: fst(t)
, 
implies: P 
⇒ Q
, 
run_local_pred: run_local_pred(r;e)
, 
member: t ∈ T
, 
prop: ℙ
, 
uall: ∀[x:A]. B[x]
, 
nat: ℕ
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
run-local-pred: run-local-pred(r;i;t;t')
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
ifthenelse: if b then t else f fi 
, 
ge: i ≥ j 
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
not: ¬A
, 
top: Top
, 
bfalse: ff
, 
or: P ∨ Q
, 
sq_type: SQType(T)
, 
guard: {T}
, 
bnot: ¬bb
, 
assert: ↑b
, 
le: A ≤ B
, 
less_than': less_than'(a;b)
, 
int_upper: {i...}
, 
has-value: (a)↓
, 
decidable: Dec(P)
, 
subtype_rel: A ⊆r B
, 
nequal: a ≠ b ∈ T 
, 
rev_uimplies: rev_uimplies(P;Q)
, 
Id: Id
, 
true: True
Latex:
\mforall{}M:Type  {}\mrightarrow{}  Type.  \mforall{}r:pRunType(P.M[P]).  \mforall{}e,x:runEvents(r).
    ((run-event-loc(x)  =  run-event-loc(e))
    {}\mRightarrow{}  run-event-step(x)  <  run-event-step(e)
    {}\mRightarrow{}  run-event-step(run\_local\_pred(r;e))  <  run-event-step(e))
Date html generated:
2016_05_17-AM-10_49_54
Last ObjectModification:
2016_01_18-AM-00_15_10
Theory : process-model
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