Nuprl Lemma : member-cut-add-at
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀f:sys-antecedent(es;X). ∀c:Cut(X;f). ∀e,a:E(X). ∀j:Id.
((a ∈ c+e(j)) ⇐⇒ (a ∈ c(j)) ∨ ((loc(e) = j ∈ Id) ∧ (a = e ∈ E(X))))
Proof
Definitions occuring in Statement :
es-cut-add: c+e,
es-cut-at: c(i),
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-loc: loc(e),
Id: Id,
l_member: (x ∈ l),
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
member: t ∈ T,
es-cut: Cut(X;f),
es-cut-add: c+e,
es-cut-at: c(i),
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
es-E-interface: E(X),
uimplies: b supposing a,
or: P ∨ Q,
uiff: uiff(P;Q),
prop: ℙ,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
decidable: Dec(P),
so_apply: x[s],
so_lambda: λ2x.t[x],
cand: A c∧ B,
guard: {T},
false: False,
not: ¬A
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,a:E(X). \mforall{}j:Id.
((a \mmember{} c+e(j)) \mLeftarrow{}{}\mRightarrow{} (a \mmember{} c(j)) \mvee{} ((loc(e) = j) \mwedge{} (a = e)))
Date html generated:
2016_05_17-AM-07_37_01
Last ObjectModification:
2015_12_28-PM-11_51_14
Theory : event-ordering
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