Nuprl Lemma : State-loc-comb-classrel2
∀[Info,B,A:Type]. ∀[f:Id ⟶ A ⟶ B ⟶ B]. ∀[init:Id ⟶ bag(B)].
∀X:EClass(A). ∀es:EO+(Info). ∀e:E.
∀[v:B]. (v ∈ State-loc-comb(init;f;X)(e) ⇐⇒ ↓iterated-classrel(es;B;A;f loc(e);init;X;e;v))
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),
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,
squash: ↓T,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
bag: bag(T)
Definitions unfolded in proof :
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
rev_implies: P ⇐ Q,
all: ∀x:A. B[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
squash: ↓T,
classrel: v ∈ X(e),
bag-member: x ↓∈ bs
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]. (v \mmember{} State-loc-comb(init;f;X)(e) \mLeftarrow{}{}\mRightarrow{} \mdownarrow{}iterated-classrel(es;B;A;f loc(e);init;X;e;v))
Date html generated:
2016_05_17-AM-10_01_30
Last ObjectModification:
2016_01_17-PM-11_04_57
Theory : classrel!lemmas
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