Nuprl Lemma : cut-list-maximal-exists
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀f:sys-antecedent(es;X). ∀a:E(X) List.
((¬(a = {} ∈ fset(E(X))))
⇒ (∃e:E(X)
((e ∈ a)
∧ (∀e':E(X). ((e' ∈ a) ⇒ (e = (X-pred e') ∈ E(X)) ⇒ (e' = e ∈ E(X))))
∧ (∀e':E(X). ((e' ∈ a) ⇒ (e = (f e') ∈ E(X)) ⇒ (e' = e ∈ E(X)))))))
Proof
Definitions occuring in Statement :
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),
empty-fset: {},
fset: fset(T),
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
apply: f a,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
or: P ∨ Q,
cons: [a / b],
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
not: ¬A,
empty-fset: {},
false: False,
so_lambda: λ2x.t[x],
and: P ∧ Q,
so_apply: x[s],
sys-antecedent: sys-antecedent(es;Sys),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B,
decidable: Dec(P),
exists: ∃x:A. B[x],
guard: {T},
es-E-interface: E(X),
top: Top,
ge: i ≥ j ,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
sq_stable: SqStable(P),
squash: ↓T,
l_member: (x ∈ l),
nat: ℕ,
true: True,
es-causle: e c≤ e',
label: ...$L... t,
sq_type: SQType(T),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
es-interface-pred: X-pred,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
bfalse: ff,
bnot: ¬bb
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}f:sys-antecedent(es;X). \mforall{}a:E(X) List.
((\mneg{}(a = \{\}))
{}\mRightarrow{} (\mexists{}e:E(X)
((e \mmember{} a)
\mwedge{} (\mforall{}e':E(X). ((e' \mmember{} a) {}\mRightarrow{} (e = (X-pred e')) {}\mRightarrow{} (e' = e)))
\mwedge{} (\mforall{}e':E(X). ((e' \mmember{} a) {}\mRightarrow{} (e = (f e')) {}\mRightarrow{} (e' = e))))))
Date html generated:
2016_05_17-AM-07_38_30
Last ObjectModification:
2016_01_17-PM-03_07_06
Theory : event-ordering
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