Nuprl Lemma : es-cut-add-at
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[f:sys-antecedent(es;X)]. ∀[c:Cut(X;f)]. ∀[e:E(X)].
((c+e(loc(e)) = (c(loc(e)) @ [e]) ∈ ({e':E(X)| loc(e') = loc(e) ∈ Id} List))
∧ (c+e(loc(e)) = ≤(X)(e) ∈ ({e':E(X)| loc(e') = loc(e) ∈ Id} List))
∧ (∀[i:Id]. c+e(i) = c(i) ∈ ({e:E(X)| loc(e) = i ∈ Id} List) supposing ¬(i = loc(e) ∈ Id))) supposing
((¬e ∈ c) and
((↑e ∈b prior(X)) ⇒ prior(X)(e) ∈ c) and
((¬((f e) = e ∈ E(X))) ⇒ f e ∈ c))
Proof
Definitions occuring in Statement :
es-cut-add: c+e,
es-cut-at: c(i),
es-cut: Cut(X;f),
es-prior-interface: prior(X),
es-interface-predecessors: ≤(X)(e),
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),
es-loc: loc(e),
Id: Id,
fset-member: a ∈ s,
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
apply: f a,
universe: Type,
equal: s = t ∈ T
Lemmas :
sorted-by-unique,
es-E-interface_wf,
Id_wf,
es-loc_wf,
event-ordering+_subtype,
es-le_wf,
append_wf,
es-cut-at_wf,
cons_wf,
nil_wf,
es-le_transitivity,
set_wf,
in-eclass_wf,
sq_stable__assert,
es-causle_antisymmetry,
es-causle_weakening_locl,
assert_wf,
equal_wf,
es-cut-at-property,
member_singleton,
l_member_wf,
or_wf,
subtype_rel_list,
iff_wf,
fset-member_wf-cut,
member_append,
l_member-settype,
fset-member_wf,
es-E_wf,
es-eq_wf,
fset-member_witness,
member-fset-union,
es-eq_wf-interface,
fset-singleton_wf,
member-fset-singleton,
es-cut-at-property1,
l_all_iff,
es-le-not-locl,
es-locl_wf,
es-cut-locl-closed,
sorted-by-append1,
no_repeats-settype,
no_repeats-append,
no_repeats_singleton,
l_disjoint_singleton,
no_repeats_wf,
not_wf,
es-interface-predecessors_wf,
es-interface-predecessors-sorted-by-le,
es-interface-predecessors-no_repeats2,
member-interface-predecessors,
fset-union_wf,
es-le-self,
and_wf,
decidable__es-le,
decidable__es-locl,
es-is-prior-interface,
assert_elim,
subtype_base_sq,
bool_wf,
bool_subtype_base,
es-le-prior-interface-val,
es-cut-le-closed,
eclass-val_wf2,
es-prior-interface_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:E(X)].
((c+e(loc(e)) = (c(loc(e)) @ [e]))
\mwedge{} (c+e(loc(e)) = \mleq{}(X)(e))
\mwedge{} (\mforall{}[i:Id]. c+e(i) = c(i) supposing \mneg{}(i = loc(e)))) supposing
((\mneg{}e \mmember{} c) and
((\muparrow{}e \mmember{}\msubb{} prior(X)) {}\mRightarrow{} prior(X)(e) \mmember{} c) and
((\mneg{}((f e) = e)) {}\mRightarrow{} f e \mmember{} c))
Date html generated:
2015_07_21-PM-04_00_45
Last ObjectModification:
2015_01_27-PM-06_07_42
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