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
Lemmas :
fset-closed_wf,
cons_wf,
es-interface-pred_wf2,
nil_wf,
all_wf,
es-E-interface_wf,
fset-member_wf-cut,
es-cut_wf,
sys-antecedent_wf,
eclass_wf,
top_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
sq_stable_from_decidable,
es-eq_wf-interface,
fset-remove_wf,
decidable__fset-closed,
l_all_iff,
es-interface-pred_wf,
l_member_wf,
isect_wf,
fset-member_wf,
member-fset-remove,
fset-member_witness,
equal_wf,
cons_member,
or_wf,
null_nil_lemma,
btrue_wf,
member-implies-null-eq-bfalse,
btrue_neq_bfalse
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:
2015_07_21-PM-04_01_16
Last ObjectModification:
2015_01_27-PM-05_52_40
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