Nuprl Lemma : member-es-le-before2
∀es:EO. ∀e:E. ∀e':{a:E| loc(a) = loc(e) ∈ Id} . ((e' ∈ ≤loc(e)) ⇐⇒ e' ≤loc e )
Proof
Definitions occuring in Statement :
es-le-before: ≤loc(e),
es-le: e ≤loc e' ,
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
l_member: (x ∈ l),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
set: {x:A| B[x]} ,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
l_member: (x ∈ l),
exists: ∃x:A. B[x],
cand: A c∧ B,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
nat: ℕ,
uimplies: b supposing a,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
rev_implies: P ⇐ Q
Latex:
\mforall{}es:EO. \mforall{}e:E. \mforall{}e':\{a:E| loc(a) = loc(e)\} . ((e' \mmember{} \mleq{}loc(e)) \mLeftarrow{}{}\mRightarrow{} e' \mleq{}loc e )
Date html generated:
2016_05_16-AM-09_30_41
Last ObjectModification:
2016_01_17-PM-01_29_28
Theory : new!event-ordering
Home
Index