Nuprl Lemma : cut-of-closed
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[f:sys-antecedent(es;X)]. ∀[s:fset(E(X))]. ∀[e:E(X)].
f e ∈ cut(X;f;s) ∧ prior(X)(e) ∈ cut(X;f;s) supposing ↑e ∈b prior(X) ∧ e ∈ cut(X;f;s) supposing e ∈ s
Proof
Definitions occuring in Statement :
cut-of: cut(X;f;s),
es-prior-interface: prior(X),
sys-antecedent: sys-antecedent(es;Sys),
es-E-interface: E(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-eq: es-eq(es),
fset-member: a ∈ s,
fset: fset(T),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
and: P ∧ Q,
apply: f a,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
sys-antecedent: sys-antecedent(es;Sys),
subtype_rel: A ⊆r B,
es-cut: Cut(X;f),
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
top: Top,
es-E-interface: E(X),
so_apply: x[s],
cand: A c∧ B,
guard: {T},
sq_stable: SqStable(P),
squash: ↓T,
f-subset: xs ⊆ ys,
fset-closed: (s closed under fs),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
or: P ∨ Q,
es-interface-pred: X-pred,
not: ¬A,
false: False,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[f:sys-antecedent(es;X)]. \mforall{}[s:fset(E(X))].
\mforall{}[e:E(X)].
f e \mmember{} cut(X;f;s) \mwedge{} prior(X)(e) \mmember{} cut(X;f;s) supposing \muparrow{}e \mmember{}\msubb{} prior(X) \mwedge{} e \mmember{} cut(X;f;s)
supposing e \mmember{} s
Date html generated:
2016_05_17-AM-07_32_22
Last ObjectModification:
2016_01_17-PM-02_58_49
Theory : event-ordering
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