Nuprl Lemma : local-simulation-E-subtype
∀[f:Name ⟶ Type]. ∀[Info:Type]. ∀[es:EO+(Message(f))]. ∀[hdr:Name]. ∀[locs:bag(Id)].
∀[e1,e2:E]. (e1 ≤loc e2 ⇒ (E ⊆r E)) supposing hdr encodes Id × Info
Proof
Definitions occuring in Statement :
local-simulation-eo: local-simulation-eo(es;e;hdr;locs),
encodes-msg-type: hdr encodes T,
Message: Message(f),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-E: E,
Id: Id,
name: Name,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
local-simulation-eo: local-simulation-eo(es;e;hdr;locs),
top: Top,
true: True,
prop: ℙ,
guard: {T},
encodes-msg-type: hdr encodes T,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
less_than: a < b
Latex:
\mforall{}[f:Name {}\mrightarrow{} Type]. \mforall{}[Info:Type]. \mforall{}[es:EO+(Message(f))]. \mforall{}[hdr:Name]. \mforall{}[locs:bag(Id)].
\mforall{}[e1,e2:E]. (e1 \mleq{}loc e2 {}\mRightarrow{} (E \msubseteq{}r E)) supposing hdr encodes Id \mtimes{} Info
Date html generated:
2016_05_17-AM-08_53_34
Last ObjectModification:
2016_01_17-PM-08_33_14
Theory : messages
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