Nuprl Lemma : decidable__exists-prior-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. prior-iterated-classrel(es;A;S;v;X;f;init;e)))
Proof
Definitions occuring in Statement :
prior-iterated-classrel: prior-iterated-classrel(es;A;S;s;X;f;init;e),
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,
prior-iterated-classrel: prior-iterated-classrel(es;A;S;s;X;f;init;e),
member: t ∈ T,
subtype_rel: A ⊆r B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
assert: ↑b,
ifthenelse: if b then t else f fi ,
decidable: Dec(P),
or: P ∨ Q,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
false: False,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
cand: A c∧ B,
true: True,
not: ¬A,
so_lambda: λ2x.t[x],
so_apply: x[s],
squash: ↓T,
es-E: E,
es-base-E: es-base-E(es),
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. prior-iterated-classrel(es;A;S;v;X;f;init;e)))
Date html generated:
2016_05_16-PM-01_55_52
Last ObjectModification:
2016_01_17-PM-07_41_32
Theory : event-ordering
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