Nuprl Lemma : loop-class-state-exists
∀[Info,B:Type]. ∀[X:EClass(B ⟶ B)]. ∀[init:Id ⟶ bag(B)]. ∀[es:EO+(Info)]. ∀[e:E].
uiff(0 < #(init loc(e));↓∃v:B. v ∈ loop-class-state(X;init)(e))
Proof
Definitions occuring in Statement :
loop-class-state: loop-class-state(X;init),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
less_than: a < b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type,
bag-size: #(bs),
bag: bag(T)
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
uall: ∀[x:A]. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
uiff: uiff(P;Q),
squash: ↓T,
so_lambda: λ2x.t[x],
so_apply: x[s],
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
iff: P ⇐⇒ Q,
loop-class-state: loop-class-state(X;init),
rev_uimplies: rev_uimplies(P;Q),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
cand: A c∧ B,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
true: True,
rev_implies: P ⇐ Q,
es-p-local-pred: es-p-local-pred(es;P),
es-locl: (e <loc e'),
Id: Id
Latex:
\mforall{}[Info,B:Type]. \mforall{}[X:EClass(B {}\mrightarrow{} B)]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
uiff(0 < \#(init loc(e));\mdownarrow{}\mexists{}v:B. v \mmember{} loop-class-state(X;init)(e))
Date html generated:
2016_05_16-PM-11_34_58
Last ObjectModification:
2016_01_17-PM-07_13_35
Theory : event-ordering
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