Nuprl Lemma : loop-class_wf
∀[Info,B:Type]. ∀[X:EClass(B ⟶ bag(B))]. ∀[init:Id ⟶ bag(B)].  (loop-class(X;init) ∈ EClass(B))
Proof
Definitions occuring in Statement : 
loop-class: loop-class(X;init)
, 
eclass: EClass(A[eo; e])
, 
Id: Id
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
, 
universe: Type
, 
bag: bag(T)
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
eclass: EClass(A[eo; e])
, 
all: ∀x:A. B[x]
, 
subtype_rel: A ⊆r B
, 
strongwellfounded: SWellFounded(R[x; y])
, 
exists: ∃x:A. B[x]
, 
nat: ℕ
, 
implies: P 
⇒ Q
, 
false: False
, 
ge: i ≥ j 
, 
uimplies: b supposing a
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
not: ¬A
, 
top: Top
, 
and: P ∧ Q
, 
prop: ℙ
, 
guard: {T}
, 
int_seg: {i..j-}
, 
lelt: i ≤ j < k
, 
le: A ≤ B
, 
less_than': less_than'(a;b)
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
less_than: a < b
, 
squash: ↓T
, 
loop-class: loop-class(X;init)
, 
eclass2: (X o Y)
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
primed-class-opt: Prior(X)?b
, 
class-ap: X(e)
, 
sq_exists: ∃x:{A| B[x]}
Latex:
\mforall{}[Info,B:Type].  \mforall{}[X:EClass(B  {}\mrightarrow{}  bag(B))].  \mforall{}[init:Id  {}\mrightarrow{}  bag(B)].    (loop-class(X;init)  \mmember{}  EClass(B))
Date html generated:
2016_05_16-PM-11_33_10
Last ObjectModification:
2016_01_17-PM-07_07_28
Theory : event-ordering
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