Nuprl Lemma : State-loc-comb-classrel-single-val
∀[Info,B,A:Type].
∀f:Id ⟶ A ⟶ B ⟶ B. ∀init:Id ⟶ bag(B). ∀X:EClass(A). ∀es:EO+(Info). ∀e:E. ∀v:B.
(uiff(v ∈ State-loc-comb(init;f;X)(e);iterated-classrel(es;B;A;f loc(e);init;X;e;v))) supposing
(single-valued-classrel(es;X;A) and
single-valued-bag(init loc(e);B))
Proof
Definitions occuring in Statement :
State-loc-comb: State-loc-comb(init;f;X),
iterated-classrel: iterated-classrel(es;S;A;f;init;X;e;v),
single-valued-classrel: single-valued-classrel(es;X;T),
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),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
single-valued-bag: single-valued-bag(b;T),
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
single-valued-bag: single-valued-bag(b;T),
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
single-valued-classrel: single-valued-classrel(es;X;T),
uiff: uiff(P;Q),
and: P ∧ Q,
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
squash: ↓T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
rev_uimplies: rev_uimplies(P;Q)
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. \mforall{}v:B.
(uiff(v \mmember{} State-loc-comb(init;f;X)(e);iterated-classrel(es;B;A;f loc(e);init;X;e;v))) supposing
(single-valued-classrel(es;X;A) and
single-valued-bag(init loc(e);B))
Date html generated:
2016_05_17-AM-10_01_58
Last ObjectModification:
2016_01_17-PM-11_04_43
Theory : classrel!lemmas
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