Nuprl Lemma : nonempty-es-interface-history
∀[Info:Type]
∀es:EO+(Info)
∀[A:Type]
∀X:EClass(A List). ∀e:E.
(0 < ||es-interface-history(es;X;e)|| ⇐⇒ ∃e':E. (((↑e' ∈b X) ∧ e' ≤loc e ) ∧ 0 < ||X(e')||))
Proof
Definitions occuring in Statement :
es-interface-history: es-interface-history(es;X;e),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-E: E,
length: ||as||,
list: T List,
assert: ↑b,
less_than: a < b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
top: Top,
cand: A c∧ B,
so_apply: x[s],
listp: A List+,
or: P ∨ Q,
false: False,
cons: [a / b],
guard: {T},
nat: ℕ,
le: A ≤ B,
decidable: Dec(P),
not: ¬A,
uiff: uiff(P;Q),
subtract: n - m,
less_than': less_than'(a;b),
true: True,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[A:Type]
\mforall{}X:EClass(A List). \mforall{}e:E.
(0 < ||es-interface-history(es;X;e)||
\mLeftarrow{}{}\mRightarrow{} \mexists{}e':E. (((\muparrow{}e' \mmember{}\msubb{} X) \mwedge{} e' \mleq{}loc e ) \mwedge{} 0 < ||X(e')||))
Date html generated:
2016_05_16-PM-11_16_12
Last ObjectModification:
2016_01_17-PM-07_16_51
Theory : event-ordering
Home
Index