Nuprl Lemma : memory-classrel1-sv
∀[Info,A1,S:Type].
∀init:Id ⟶ S. ∀tr1:Id ⟶ A1 ⟶ S ⟶ S. ∀X1:EClass(A1). ∀es:EO+(Info). ∀e:E. ∀v:S.
(single-valued-classrel(es;X1;A1)
⇒ (v ∈ memory-class1(initially init
applying tr1
on X1)(e)
⇐⇒ prior-iterated-classrel(es;A1;S;v;X1;tr1 loc(e);λloc.{init loc};e)))
Proof
Definitions occuring in Statement :
memory-class1: memory-class1,
prior-iterated-classrel: prior-iterated-classrel(es;A;S;s;X;f;init;e),
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,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
apply: f a,
lambda: λx.A[x],
function: x:A ⟶ B[x],
universe: Type,
single-bag: {x}
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
true: True,
Memory1: Memory1(init;tr;X),
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
uimplies: b supposing a,
uiff: uiff(P;Q),
squash: ↓T,
guard: {T}
Latex:
\mforall{}[Info,A1,S:Type].
\mforall{}init:Id {}\mrightarrow{} S. \mforall{}tr1:Id {}\mrightarrow{} A1 {}\mrightarrow{} S {}\mrightarrow{} S. \mforall{}X1:EClass(A1). \mforall{}es:EO+(Info). \mforall{}e:E. \mforall{}v:S.
(single-valued-classrel(es;X1;A1)
{}\mRightarrow{} (v \mmember{} memory-class1(initially init
applying tr1
on X1)(e)
\mLeftarrow{}{}\mRightarrow{} prior-iterated-classrel(es;A1;S;v;X1;tr1 loc(e);\mlambda{}loc.\{init loc\};e)))
Date html generated:
2016_05_17-AM-10_06_41
Last ObjectModification:
2016_01_17-PM-11_03_27
Theory : classrel!lemmas
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