Nuprl Lemma : run_local_pred_loc
∀[M:Type ⟶ Type]. ∀r:pRunType(P.M[P]). ∀e:runEvents(r). ((snd(run_local_pred(r;e))) = (snd(e)) ∈ Id)
Proof
Definitions occuring in Statement :
run_local_pred: run_local_pred(r;e),
runEvents: runEvents(r),
pRunType: pRunType(T.M[T]),
Id: Id,
uall: ∀[x:A]. B[x],
so_apply: x[s],
pi2: snd(t),
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
runEvents: runEvents(r),
run_local_pred: run_local_pred(r;e),
pi1: fst(t),
pi2: snd(t),
so_lambda: λ2x.t[x],
so_apply: x[s],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
run-local-pred: run-local-pred(r;i;t;t'),
eq_int: (i =z j),
subtract: n - m,
ifthenelse: if b then t else f fi ,
btrue: tt,
decidable: Dec(P),
or: P ∨ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
has-value: (a)↓,
nequal: a ≠ b ∈ T ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]. \mforall{}r:pRunType(P.M[P]). \mforall{}e:runEvents(r). ((snd(run\_local\_pred(r;e))) = (snd(e)))
Date html generated:
2016_05_17-AM-10_49_41
Last ObjectModification:
2016_01_18-AM-00_12_56
Theory : process-model
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