Nuprl Lemma : stdEO-causal
∀[M:Type ⟶ Type]
∀[S0:InitialSystem(P.M[P])]. ∀[n2m:ℕ ⟶ pMsg(P.M[P])]. ∀[l2m:Id ⟶ pMsg(P.M[P])]. ∀[env:pEnvType(P.M[P])]. ∀[e1,e2:E].
run-event-step(e1) < run-event-step(e2) supposing (e1 < e2)
supposing Continuous+(P.M[P])
Proof
Definitions occuring in Statement :
stdEO: stdEO(n2m;l2m;env;S),
InitialSystem: InitialSystem(P.M[P]),
run-event-step: run-event-step(e),
pEnvType: pEnvType(T.M[T]),
pMsg: pMsg(P.M[P]),
es-causl: (e < e'),
es-E: E,
Id: Id,
strong-type-continuous: Continuous+(T.F[T]),
nat: ℕ,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
prop: ℙ,
all: ∀x:A. B[x],
eo_axioms: eo_axioms(r),
and: P ∧ Q,
stdEO: stdEO(n2m;l2m;env;S),
runEO: runEO(n2m;l2m;env;S),
run-eo: EO(r),
mk-extended-eo: mk-extended-eo,
top: Top,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
mk-eo: mk-eo(E;dom;l;R;locless;pred;rank),
mk-eo-record: mk-eo-record(E;dom;l;R;locless;pred;rank),
btrue: tt,
es-causl: (e < e'),
es-E: E,
assert: ↑b,
implies: P ⇒ Q
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}[S0:InitialSystem(P.M[P])]. \mforall{}[n2m:\mBbbN{} {}\mrightarrow{} pMsg(P.M[P])]. \mforall{}[l2m:Id {}\mrightarrow{} pMsg(P.M[P])].
\mforall{}[env:pEnvType(P.M[P])]. \mforall{}[e1,e2:E].
run-event-step(e1) < run-event-step(e2) supposing (e1 < e2)
supposing Continuous+(P.M[P])
Date html generated:
2016_05_17-AM-10_52_36
Last ObjectModification:
2015_12_29-PM-05_19_23
Theory : process-model
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