Nuprl Lemma : loop-class-memory-size-zero
∀[Info,B:Type]. ∀[X:EClass(B ⟶ B)]. ∀[init:Id ⟶ bag(B)]. ∀[es:EO+(Info)]. ∀[e:E].
uiff(#(init loc(e)) = 0 ∈ ℤ;#(loop-class-memory(X;init)(e)) = 0 ∈ ℤ)
Proof
Definitions occuring in Statement :
loop-class-memory: loop-class-memory(X;init),
class-ap: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T,
bag-size: #(bs),
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
prop: ℙ,
nat: ℕ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
guard: {T},
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top
Latex:
\mforall{}[Info,B:Type]. \mforall{}[X:EClass(B {}\mrightarrow{} B)]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
uiff(\#(init loc(e)) = 0;\#(loop-class-memory(X;init)(e)) = 0)
Date html generated:
2016_05_16-PM-11_38_19
Last ObjectModification:
2016_01_17-PM-07_07_13
Theory : event-ordering
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