Nuprl Lemma : es-causl_weakening_p-locl
∀es:EO. ∀p:E ⟶ (E + Top). (causal-predecessor(es;p) ⇒ (∀e,e':E. (e p< e' ⇒ (e < e'))))
Proof
Definitions occuring in Statement :
es-p-locl: e p< e',
causal-predecessor: causal-predecessor(es;p),
es-causl: (e < e'),
es-E: E,
event_ordering: EO,
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
union: left + right
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
es-p-locl: e p< e',
exists: ∃x:A. B[x],
nat_plus: ℕ+,
so_lambda: λ2x.t[x],
so_apply: x[s],
p-fun-exp: f^n,
p-graph: p-graph(A;f),
top: Top,
p-id: p-id(),
p-compose: f o g,
do-apply: do-apply(f;x),
can-apply: can-apply(f;x),
isl: isl(x),
outl: outl(x),
ifthenelse: if b then t else f fi ,
btrue: tt,
cand: A c∧ B,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
causal-predecessor: causal-predecessor(es;p),
and: P ∧ Q,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
sq_type: SQType(T),
assert: ↑b,
true: True,
le: A ≤ B,
less_than': less_than'(a;b),
squash: ↓T,
uiff: uiff(P;Q),
iff: P ⇐⇒ Q,
bfalse: ff,
rev_uimplies: rev_uimplies(P;Q),
bool: 𝔹,
unit: Unit,
it: ⋅,
bnot: ¬bb
Latex:
\mforall{}es:EO. \mforall{}p:E {}\mrightarrow{} (E + Top). (causal-predecessor(es;p) {}\mRightarrow{} (\mforall{}e,e':E. (e p< e' {}\mRightarrow{} (e < e'))))
Date html generated:
2016_05_16-AM-10_31_30
Last ObjectModification:
2016_01_17-PM-01_26_45
Theory : new!event-ordering
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