Nuprl Lemma : cut-of-closed
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[f:sys-antecedent(es;X)]. ∀[s:fset(E(X))]. ∀[e:E(X)].
f e ∈ cut(X;f;s) ∧ prior(X)(e) ∈ cut(X;f;s) supposing ↑e ∈b prior(X) ∧ e ∈ cut(X;f;s) supposing e ∈ s
Proof
Definitions occuring in Statement :
cut-of: cut(X;f;s),
es-prior-interface: prior(X),
sys-antecedent: sys-antecedent(es;Sys),
es-E-interface: E(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-eq: es-eq(es),
fset-member: a ∈ s,
fset: fset(T),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
and: P ∧ Q,
apply: f a,
universe: Type
Lemmas :
cut-of-property,
fset_wf,
es-E-interface_wf,
sys-antecedent_wf,
eclass_wf,
top_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
cut-of_wf,
es-cut_wf,
f-subset_wf,
es-eq_wf-interface,
all_wf,
fset-member_wf,
assert_wf,
in-eclass_wf,
es-prior-interface_wf0,
es-interface-subtype_rel2,
subtype_top,
eclass-val_wf2,
es-prior-interface_wf,
isect_wf,
squash_wf,
fset-member_witness,
sq_stable__all,
sq_stable__and,
sq_stable_from_decidable,
decidable__fset-member,
sq_stable__uall,
and_wf,
equal_wf,
fset-member_wf-cut,
l_all_iff,
cons_wf,
es-interface-pred_wf,
nil_wf,
l_member_wf,
cons_member,
bool_wf,
equal-wf-T-base,
bnot_wf,
not_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[f:sys-antecedent(es;X)]. \mforall{}[s:fset(E(X))].
\mforall{}[e:E(X)].
f e \mmember{} cut(X;f;s) \mwedge{} prior(X)(e) \mmember{} cut(X;f;s) supposing \muparrow{}e \mmember{}\msubb{} prior(X) \mwedge{} e \mmember{} cut(X;f;s)
supposing e \mmember{} s
Date html generated:
2015_07_21-PM-03_58_13
Last ObjectModification:
2015_01_27-PM-05_54_17
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