Nuprl Lemma : sq_stable__iterated_classrel
∀[Info,A,S:Type]. ∀[init:Id ⟶ bag(S)]. ∀[f:A ⟶ S ⟶ S]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:S].
SqStable(iterated_classrel(es;S;A;f;init;X;e;v))
Proof
Definitions occuring in Statement :
iterated_classrel: iterated_classrel(es;S;A;f;init;X;e;v),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
iterated_classrel: iterated_classrel(es;S;A;f;init;X;e;v),
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
uimplies: b supposing a,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,A,S:Type]. \mforall{}[init:Id {}\mrightarrow{} bag(S)]. \mforall{}[f:A {}\mrightarrow{} S {}\mrightarrow{} S]. \mforall{}[X:EClass(A)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
\mforall{}[v:S].
SqStable(iterated\_classrel(es;S;A;f;init;X;e;v))
Date html generated:
2016_05_16-PM-01_47_28
Last ObjectModification:
2015_12_29-PM-02_14_26
Theory : event-ordering
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