Nuprl Lemma : hdf-ap-invariant
∀[A,B:Type]. ∀[Q:bag(B) ⟶ ℙ]. ∀[X:{X:hdataflow(A;B)| hdf-invariant(A;b.Q[b];X)} ]. ∀[a:A].
(fst(X(a)) ∈ {X:hdataflow(A;B)| hdf-invariant(A;b.Q[b];X)} )
Proof
Definitions occuring in Statement :
hdf-invariant: hdf-invariant(A;b.Q[b];X),
hdf-ap: X(a),
hdataflow: hdataflow(A;B),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
pi1: fst(t),
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top,
hdf-invariant: hdf-invariant(A;b.Q[b];X),
prop: ℙ
Latex:
\mforall{}[A,B:Type]. \mforall{}[Q:bag(B) {}\mrightarrow{} \mBbbP{}]. \mforall{}[X:\{X:hdataflow(A;B)| hdf-invariant(A;b.Q[b];X)\} ]. \mforall{}[a:A].
(fst(X(a)) \mmember{} \{X:hdataflow(A;B)| hdf-invariant(A;b.Q[b];X)\} )
Date html generated:
2016_05_16-AM-10_38_46
Last ObjectModification:
2015_12_28-PM-07_44_25
Theory : halting!dataflow
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