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),
fset-member: a ∈ s,
Id: Id,
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
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
subtype_rel: A ⊆r B,
es-cut: Cut(X;f),
so_lambda: λ2x.t[x],
sys-antecedent: sys-antecedent(es;Sys),
so_apply: x[s],
es-E-interface: E(X),
and: P ∧ Q,
cand: A c∧ B,
prop: ℙ,
implies: P ⇒ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
trans: Trans(T;x,y.E[x; y]),
guard: {T},
anti_sym: AntiSym(T;x,y.R[x; y]),
sq_stable: SqStable(P),
squash: ↓T,
set-equal: set-equal(T;x;y),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
or: P ∨ Q,
es-cut-add: c+e,
uiff: uiff(P;Q),
not: ¬A,
false: False,
rev_uimplies: rev_uimplies(P;Q),
decidable: Dec(P),
es-le: e ≤loc e' ,
exists: ∃x:A. B[x],
sq_type: SQType(T),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True
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:
2016_05_17-AM-07_36_33
Last ObjectModification:
2016_01_17-PM-03_08_22
Theory : event-ordering
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