Nuprl Lemma : State-loc-comb-non-empty-iff
∀[Info,B,A:Type]. ∀[f:Id ─→ A ─→ B ─→ B]. ∀[init:Id ─→ bag(B)].
∀X:EClass(A). ∀es:EO+(Info). ∀e:E. (¬↑bag-null(init loc(e)) ⇐⇒ ↓∃v:B. v ∈ State-loc-comb(init;f;X)(e))
Proof
Definitions occuring in Statement :
State-loc-comb: State-loc-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,
assert: ↑b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
squash: ↓T,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
bag-null: bag-null(bs),
bag: bag(T)
Lemmas :
State-loc-comb-non-empty,
not_wf,
assert_wf,
bag-null_wf,
es-loc_wf,
State-loc-comb-classrel-non-loc,
classrel_wf,
State-comb_wf,
State-comb-exists-iff,
null-bag-size,
neg_assert_of_eq_int,
bag-size_wf,
nat_wf,
squash_wf,
exists_wf,
State-loc-comb_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf,
Id_wf,
bag_wf
Latex:
\mforall{}[Info,B,A:Type]. \mforall{}[f:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[init:Id {}\mrightarrow{} bag(B)].
\mforall{}X:EClass(A). \mforall{}es:EO+(Info). \mforall{}e:E.
(\mneg{}\muparrow{}bag-null(init loc(e)) \mLeftarrow{}{}\mRightarrow{} \mdownarrow{}\mexists{}v:B. v \mmember{} State-loc-comb(init;f;X)(e))
Date html generated:
2015_07_22-PM-00_23_47
Last ObjectModification:
2015_01_28-AM-10_11_09
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