Nuprl Lemma : p-compose-causal-predecessor1
∀es:EO. ∀p,w:E ⟶ (E + Top).
(causal-predecessor(es;p) ⇒ causal-weak-predecessor(es;w) ⇒ causal-predecessor(es;p o w))
Proof
Definitions occuring in Statement :
causal-weak-predecessor: causal-weak-predecessor(es;p),
causal-predecessor: causal-predecessor(es;p),
es-E: E,
event_ordering: EO,
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
union: left + right,
p-compose: f o g
Definitions unfolded in proof :
causal-predecessor: causal-predecessor(es;p),
causal-weak-predecessor: causal-weak-predecessor(es;p),
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
top: Top,
can-apply: can-apply(f;x),
p-compose: f o g,
do-apply: do-apply(f;x),
isl: isl(x),
outl: outl(x),
ifthenelse: if b then t else f fi ,
btrue: tt,
assert: ↑b,
true: True,
bfalse: ff,
false: False,
guard: {T}
Latex:
\mforall{}es:EO. \mforall{}p,w:E {}\mrightarrow{} (E + Top).
(causal-predecessor(es;p) {}\mRightarrow{} causal-weak-predecessor(es;w) {}\mRightarrow{} causal-predecessor(es;p o w))
Date html generated:
2016_05_16-AM-10_29_35
Last ObjectModification:
2015_12_28-PM-09_16_27
Theory : new!event-ordering
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