Nuprl Lemma : State-comb-exists-iff
∀[Info,B,A:Type]. ∀[f:A ─→ B ─→ B]. ∀[init:Id ─→ bag(B)].
∀X:EClass(A). ∀[es:EO+(Info)]. ∀[e:E]. uiff(#(init loc(e)) > 0;↓∃v:B. v ∈ State-comb(init;f;X)(e))
Proof
Definitions occuring in Statement :
State-comb: State-comb(init;f;X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
gt: i > j,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
apply: f a,
function: x:A ─→ B[x],
natural_number: $n,
universe: Type,
bag-size: #(bs),
bag: bag(T)
Lemmas :
primed-class-opt-classrel,
State-comb_wf,
es-causl_weakening,
event-ordering+_subtype,
classrel_wf,
and_wf,
equal_wf,
Id_wf,
bag_wf,
bag-size_wf,
nat_wf,
less_than_wf,
bag-member-iff-size,
es-loc_wf,
bag-member_wf,
bag-member-lifting-2,
primed-class-opt_wf,
eclass_wf,
es-E_wf,
event-ordering+_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]. uiff(\#(init loc(e)) > 0;\mdownarrow{}\mexists{}v:B. v \mmember{} State-comb(init;f;X)(e))
Date html generated:
2015_07_22-PM-00_20_55
Last ObjectModification:
2015_01_28-AM-10_14_32
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