Nuprl Lemma : State-comb-top
∀[Info,A:Type]. ∀[es:EO+(Info)]. ∀[f:Top]. ∀[X:EClass(A)]. ∀[init:Id ⟶ bag(Top)]. (State-comb(init;f;X) ∈ EClass(Top))
Proof
Definitions occuring in Statement :
State-comb: State-comb(init;f;X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type,
bag: bag(T)
Definitions unfolded in proof :
State-comb: State-comb(init;f;X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
prop: ℙ,
lifting-2: lifting-2(f),
lifting2: lifting2(f;abag;bbag),
lifting-gen-rev: lifting-gen-rev(n;f;bags),
lifting-gen-list-rev: lifting-gen-list-rev(n;bags),
eq_int: (i =z j),
select: L[n],
cons: [a / b],
ifthenelse: if b then t else f fi ,
bfalse: ff,
subtract: n - m,
btrue: tt,
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q
Latex:
\mforall{}[Info,A:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[f:Top]. \mforall{}[X:EClass(A)]. \mforall{}[init:Id {}\mrightarrow{} bag(Top)].
(State-comb(init;f;X) \mmember{} EClass(Top))
Date html generated:
2016_05_17-AM-09_59_14
Last ObjectModification:
2015_12_29-PM-03_55_59
Theory : classrel!lemmas
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