Nuprl Lemma : es-cut-remove
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[f:sys-antecedent(es;X)]. ∀[c:Cut(X;f)]. ∀[e:E(X)].
fset-remove(es-eq(es);e;c) ∈ Cut(X;f) supposing ∀e':E(X). (e' ∈ c ⇒ (¬(e < e')))
Proof
Definitions occuring in Statement :
es-cut: Cut(X;f),
sys-antecedent: sys-antecedent(es;Sys),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-eq: es-eq(es),
es-causl: (e < e'),
fset-remove: fset-remove(eq;y;s),
fset-member: a ∈ s,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
es-cut: Cut(X;f),
sys-antecedent: sys-antecedent(es;Sys),
prop: ℙ,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
es-E-interface: E(X),
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
sq_stable: SqStable(P),
fset-closed: (s closed under fs),
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
cand: A c∧ B,
squash: ↓T,
or: P ∨ Q,
guard: {T},
not: ¬A,
false: False,
es-causle: e c≤ e',
label: ...$L... t,
sq_type: SQType(T),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[f:sys-antecedent(es;X)]. \mforall{}[c:Cut(X;f)].
\mforall{}[e:E(X)].
fset-remove(es-eq(es);e;c) \mmember{} Cut(X;f) supposing \mforall{}e':E(X). (e' \mmember{} c {}\mRightarrow{} (\mneg{}(e < e')))
Date html generated:
2016_05_17-AM-07_37_52
Last ObjectModification:
2016_01_17-PM-02_50_55
Theory : event-ordering
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