Nuprl Lemma : Accum-loc-class-exists
∀[Info,B,A:Type]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[f:Id ⟶ A ⟶ B ⟶ B]. ∀[init:Id ⟶ bag(B)]. ∀[X:EClass(A)].
((↓∃x:B. x ↓∈ init loc(e)) ⇒ (↓∃u:A. u ∈ X(e)) ⇒ (↓∃v:B. v ∈ Accum-loc-class(f;init;X)(e)))
Proof
Definitions occuring in Statement :
Accum-loc-class: Accum-loc-class(f;init;X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
bag-member: x ↓∈ bs,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
squash: ↓T,
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
Accum-loc-class: Accum-loc-class(f;init;X),
top: Top,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
uimplies: b supposing a,
cand: A c∧ B,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,B,A:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[f:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[init:Id {}\mrightarrow{} bag(B)].
\mforall{}[X:EClass(A)].
((\mdownarrow{}\mexists{}x:B. x \mdownarrow{}\mmember{} init loc(e)) {}\mRightarrow{} (\mdownarrow{}\mexists{}u:A. u \mmember{} X(e)) {}\mRightarrow{} (\mdownarrow{}\mexists{}v:B. v \mmember{} Accum-loc-class(f;init;X)(e)))
Date html generated:
2016_05_17-AM-09_32_39
Last ObjectModification:
2016_01_17-PM-11_08_31
Theory : classrel!lemmas
Home
Index