Nuprl Lemma : loop-class_local
∀[Info,B:Type]. ∀[X:EClass(B ⟶ bag(B))].
∀init:Id ⟶ bag(B). LocalClass(X)
⇒ LocalClass(loop-class(X;init)) supposing valueall-type(B)
Proof
Definitions occuring in Statement :
loop-class: loop-class(X;init)
,
local-class: LocalClass(X)
,
eclass: EClass(A[eo; e])
,
Id: Id
,
valueall-type: valueall-type(T)
,
uimplies: b supposing a
,
uall: ∀[x:A]. B[x]
,
all: ∀x:A. B[x]
,
implies: P
⇒ Q
,
function: x:A ⟶ B[x]
,
universe: Type
,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
all: ∀x:A. B[x]
,
uimplies: b supposing a
,
member: t ∈ T
,
valueall-type: valueall-type(T)
,
has-value: (a)↓
,
prop: ℙ
,
implies: P
⇒ Q
,
so_lambda: λ2x y.t[x; y]
,
subtype_rel: A ⊆r B
,
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,B:Type]. \mforall{}[X:EClass(B {}\mrightarrow{} bag(B))].
\mforall{}init:Id {}\mrightarrow{} bag(B). LocalClass(X) {}\mRightarrow{} LocalClass(loop-class(X;init)) supposing valueall-type(B)
Date html generated:
2016_05_17-AM-09_06_11
Last ObjectModification:
2015_12_29-PM-03_36_20
Theory : local!classes
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