Nuprl Lemma : member-cut-add
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀f:sys-antecedent(es;X). ∀c:Cut(X;f). ∀e,a:E(X). (a ∈ c+e ⇐⇒ (a = e ∈ E(X)) ∨ a ∈ c)
Proof
Definitions occuring in Statement :
es-cut-add: c+e,
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),
fset-member: a ∈ s,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
universe: Type,
equal: s = t ∈ T
Lemmas :
or_wf,
equal_wf,
fset-member_wf-cut,
member-fset-singleton,
es-eq_wf-interface,
fset-member_wf,
fset-singleton_wf,
iff_wf,
member-fset-union,
fset-union_wf,
es-E-interface_wf,
set_wf,
fset_wf,
fset-closed_wf,
cons_wf,
es-interface-pred_wf2,
nil_wf,
sys-antecedent_wf,
eclass_wf,
top_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_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).
(a \mmember{} c+e \mLeftarrow{}{}\mRightarrow{} (a = e) \mvee{} a \mmember{} c)
Date html generated:
2015_07_21-PM-04_00_12
Last ObjectModification:
2015_01_27-PM-05_51_32
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