Nuprl Lemma : es-cut-remove-1
∀[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 = (f e') ∈ E(X)) ⇒ (e' = e ∈ E(X))))
∧ (∀e':E(X). (e' ∈ c ⇒ (e = (X-pred e') ∈ E(X)) ⇒ (e' = e ∈ E(X))))
Proof
Definitions occuring in Statement :
es-cut: Cut(X;f),
es-interface-pred: X-pred,
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),
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],
implies: P ⇒ Q,
and: P ∧ Q,
member: t ∈ T,
apply: f a,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
es-cut: Cut(X;f),
sys-antecedent: sys-antecedent(es;Sys),
prop: ℙ,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s],
all: ∀x:A. B[x],
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
sq_stable: SqStable(P),
fset-closed: (s closed under fs),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
cand: A c∧ B,
squash: ↓T,
not: ¬A,
false: False,
or: P ∨ Q,
es-E-interface: E(X),
sq_type: SQType(T),
guard: {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{} (e = (f e')) {}\mRightarrow{} (e' = e)))
\mwedge{} (\mforall{}e':E(X). (e' \mmember{} c {}\mRightarrow{} (e = (X-pred e')) {}\mRightarrow{} (e' = e)))
Date html generated:
2016_05_17-AM-07_37_26
Last ObjectModification:
2016_01_17-PM-02_52_52
Theory : event-ordering
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