Nuprl Lemma : iterated-classrel-Memory-classrel
∀[Info,B,A:Type]. ∀[f:A ─→ B ─→ B]. ∀[init:Id ─→ bag(B)].
∀X:EClass(A). ∀es:EO+(Info). ∀e:E.
∀[v:B]
uiff(iterated_classrel(es;B;A;f;init;X;e;v);↓(∃a:A
∃b:B
(a ∈ X(e) ∧ b ∈ Memory-class(f;init;X)(e) ∧ (v = (f a b) ∈ B)))
∨ ((∀a:A. (¬a ∈ X(e))) ∧ v ∈ Memory-class(f;init;X)(e)))
Proof
Definitions occuring in Statement :
Memory-class: Memory-class(f;init;X),
iterated_classrel: iterated_classrel(es;S;A;f;init;X;e;v),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
squash: ↓T,
or: P ∨ Q,
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Lemmas :
squash_wf,
exists_wf,
bag-member_wf,
es-loc_wf,
event-ordering+_subtype,
or_wf,
classrel_wf,
all_wf,
not_wf,
Memory-class_wf,
Memory-classrel1,
assert_wf,
es-first_wf2,
es-pred_wf,
and_wf,
equal_wf,
member_wf,
es-pred-locl,
es-causl_weakening,
iterated_classrel_wf,
uiff_wf,
bool_wf,
eqtt_to_assert,
uiff_transitivity,
equal-wf-T-base,
bnot_wf,
eqff_to_assert,
assert_of_bnot
Latex:
\mforall{}[Info,B,A:Type]. \mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[init:Id {}\mrightarrow{} bag(B)].
\mforall{}X:EClass(A). \mforall{}es:EO+(Info). \mforall{}e:E.
\mforall{}[v:B]
uiff(iterated\_classrel(es;B;A;f;init;X;e;v);\mdownarrow{}(\mexists{}a:A
\mexists{}b:B
(a \mmember{} X(e)
\mwedge{} b \mmember{} Memory-class(f;init;X)(e)
\mwedge{} (v = (f a b))))
\mvee{} ((\mforall{}a:A. (\mneg{}a \mmember{} X(e)))
\mwedge{} v \mmember{} Memory-class(f;init;X)(e)))
Date html generated:
2015_07_22-PM-00_12_17
Last ObjectModification:
2015_01_28-AM-11_43_35
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