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
Lemmas :
Id_wf,
es-E-interface_wf,
es-cut_wf,
sys-antecedent_wf,
eclass_wf,
top_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
es-fset-at-property,
subtype_rel_fset,
es-E-interface-strong-subtype,
fset-union_wf,
es-eq_wf,
fset-singleton_wf,
member-fset-union,
es-eq_wf-interface,
or_wf,
fset-member_wf,
es-loc_wf,
l_member_wf,
es-fset-at_wf,
member-fset-singleton,
equal_wf,
decidable__equal_es-E-interface,
and_wf,
iff_weakening_equal,
l_member-settype,
assert_wf,
in-eclass_wf,
es-fset-at_wf-interface,
list_wf,
iff_wf
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:
2015_07_21-PM-04_01_02
Last ObjectModification:
2015_02_04-PM-06_08_06
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