Nuprl Lemma : loop-class-memory-member
∀[Info,B:Type]. ∀[X:EClass(B ⟶ B)]. ∀[init:Id ⟶ bag(B)]. ∀[es:EO+(Info)]. ∀[e:E].
uiff(0 < #(init loc(e));↑e ∈b loop-class-memory(X;init))
Proof
Definitions occuring in Statement :
loop-class-memory: loop-class-memory(X;init),
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
assert: ↑b,
less_than: a < b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type,
bag-size: #(bs),
bag: bag(T)
Definitions unfolded in proof :
class-ap: X(e),
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
rev_implies: P ⇐ Q,
nat: ℕ,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
eclass: EClass(A[eo; e]),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
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(0 < \#(init loc(e));\muparrow{}e \mmember{}\msubb{} loop-class-memory(X;init))
Date html generated:
2016_05_16-PM-11_38_02
Last ObjectModification:
2015_12_29-AM-10_11_26
Theory : event-ordering
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