Nuprl Lemma : decidable__exists_iterated_classrel
∀[Info,A,S:Type].
∀init:Id ⟶ bag(S). ∀f:A ⟶ S ⟶ S. ∀X:EClass(A). ∀es:EO+(Info). ∀e:E.
(single-valued-classrel(es;X;A)
⇒ single-valued-bag(init loc(e);S)
⇒ Dec(∃v:S. iterated_classrel(es;S;A;f;init;X;e;v)))
Proof
Definitions occuring in Statement :
iterated_classrel: iterated_classrel(es;S;A;f;init;X;e;v),
single-valued-classrel: single-valued-classrel(es;X;T),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
single-valued-bag: single-valued-bag(b;T),
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
nat: ℕ,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
and: P ∧ Q,
less_than: a < b,
squash: ↓T,
le: A ≤ B,
less_than': less_than'(a;b),
uiff: uiff(P;Q),
iterated_classrel: iterated_classrel(es;S;A;f;init;X;e;v),
cand: A c∧ B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
es-E: E,
es-base-E: es-base-E(es),
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}[Info,A,S:Type].
\mforall{}init:Id {}\mrightarrow{} bag(S). \mforall{}f:A {}\mrightarrow{} S {}\mrightarrow{} S. \mforall{}X:EClass(A). \mforall{}es:EO+(Info). \mforall{}e:E.
(single-valued-classrel(es;X;A)
{}\mRightarrow{} single-valued-bag(init loc(e);S)
{}\mRightarrow{} Dec(\mexists{}v:S. iterated\_classrel(es;S;A;f;init;X;e;v)))
Date html generated:
2016_05_16-PM-01_48_41
Last ObjectModification:
2016_01_17-PM-07_44_59
Theory : event-ordering
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