Nuprl Lemma : Memory-classrel1
∀[Info,B,A:Type]. ∀[f:A ─→ B ─→ B]. ∀[init:Id ─→ bag(B)]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:B].
uiff(v ∈ Memory-class(f;init;X)(e);↓((↑first(e)) ∧ v ↓∈ init loc(e))
∨ ((¬↑first(e))
∧ ((∃a:A
(a ∈ X(pred(e))
∧ (∃b:B. (b ∈ Memory-class(f;init;X)(pred(e)) ∧ (v = (f a b) ∈ B)))))
∨ ((∀a:A. (¬a ∈ X(pred(e)))) ∧ v ∈ Memory-class(f;init;X)(pred(e))))))
Proof
Definitions occuring in Statement :
Memory-class: Memory-class(f;init;X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-first: first(e),
es-pred: pred(e),
es-loc: loc(e),
es-E: E,
Id: Id,
assert: ↑b,
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-member: x ↓∈ bs,
bag: bag(T)
Lemmas :
es-first_wf2,
event-ordering+_subtype,
bool_wf,
eqtt_to_assert,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
lt_int_wf,
bag-size_wf,
es-pred_wf,
assert_of_lt_int,
less_than_wf,
Id_wf,
atom2_subtype_base,
es-loc_wf,
es-pred-loc-base,
es-E_wf,
iff_weakening_equal,
not_wf,
true_wf,
or_wf,
exists_wf,
classrel_wf,
Memory-class_wf,
all_wf,
bag-member_wf,
squash_wf,
Accum-class_wf,
eclass_wf,
event-ordering+_wf,
nat_wf,
bag-size-bag-member,
Accum-classrel-Memory,
false_wf,
uiff_wf
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(v \mmember{} Memory-class(f;init;X)(e);\mdownarrow{}((\muparrow{}first(e)) \mwedge{} v \mdownarrow{}\mmember{} init loc(e))
\mvee{} ((\mneg{}\muparrow{}first(e))
\mwedge{} ((\mexists{}a:A
(a \mmember{} X(pred(e))
\mwedge{} (\mexists{}b:B
(b \mmember{} Memory-class(f;init;X)(pred(e))
\mwedge{} (v = (f a b))))))
\mvee{} ((\mforall{}a:A. (\mneg{}a \mmember{} X(pred(e))))
\mwedge{} v \mmember{} Memory-class(f;init;X)(pred(e))))))
Date html generated:
2015_07_22-PM-00_11_49
Last ObjectModification:
2015_02_04-PM-04_42_27
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