Nuprl Lemma : class-pred-cases
∀[Info,T:Type].
∀X:EClass(T). ∀es:EO+(Info). ∀e:E.
(∃e'<e.((↓∃v:T. v ∈ X(e')) ∧ ∀e''<e.(↓∃v:T. v ∈ X(e'')) ⇒ e'' ≤loc e' )
∧ (class-pred(X;es;e) = (inl e') ∈ (E + Top))
∨ (∀e'<e.∀v:T. (¬v ∈ X(e')) ∧ (class-pred(X;es;e) = (inr ⋅ ) ∈ (E + Top))))
Proof
Definitions occuring in Statement :
class-pred: class-pred(X;es;e),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
alle-lt: ∀e<e'.P[e],
existse-before: ∃e<e'.P[e],
es-le: e ≤loc e' ,
es-E: E,
it: ⋅,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
squash: ↓T,
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
inr: inr x ,
inl: inl x,
union: left + right,
universe: Type,
equal: s = t ∈ T
Lemmas :
bag-member-iff-size,
squash_wf,
exists_wf,
bag-member_wf,
less_than_wf,
bag-size_wf,
nat_wf,
bag_wf,
es-local-pred_wf,
lt_int_wf,
or_wf,
sq_exists_wf,
es-locl_wf,
assert_wf,
all_wf,
not_wf,
alle-lt_wf,
Id_wf,
es-loc_wf,
classrel_wf,
equal-wf-T-base,
top_wf,
subtype_rel_sum,
existse-before_wf,
es-le_wf,
equal_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf,
sq_stable_from_decidable,
decidable__es-locl,
assert_of_lt_int,
decidable__es-le,
es-le-not-locl
Latex:
\mforall{}[Info,T:Type].
\mforall{}X:EClass(T). \mforall{}es:EO+(Info). \mforall{}e:E.
(\mexists{}e'<e.((\mdownarrow{}\mexists{}v:T. v \mmember{} X(e')) \mwedge{} \mforall{}e''<e.(\mdownarrow{}\mexists{}v:T. v \mmember{} X(e'')) {}\mRightarrow{} e'' \mleq{}loc e' )
\mwedge{} (class-pred(X;es;e) = (inl e'))
\mvee{} (\mforall{}e'<e.\mforall{}v:T. (\mneg{}v \mmember{} X(e')) \mwedge{} (class-pred(X;es;e) = (inr \mcdot{} ))))
Date html generated:
2015_07_20-PM-03_58_12
Last ObjectModification:
2015_01_27-PM-10_00_33
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