Nuprl Lemma : hdf-ap-invariant2
∀[A,B:Type]. ∀[Q:bag(B) ⟶ ℙ].
(Q[{}] ⇒ (∀b:bag(B). SqStable(Q[b])) ⇒ (∀X:{X:hdataflow(A;B)| hdf-invariant(A;b.Q[b];X)} . ∀a:A. Q[snd(X(a))]))
Proof
Definitions occuring in Statement :
hdf-invariant: hdf-invariant(A;b.Q[b];X),
hdf-ap: X(a),
hdataflow: hdataflow(A;B),
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
pi2: snd(t),
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type,
empty-bag: {},
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_stable: SqStable(P),
squash: ↓T,
prop: ℙ,
hdf-invariant: hdf-invariant(A;b.Q[b];X),
top: Top,
subtype_rel: A ⊆r B,
ext-eq: A ≡ B,
and: P ∧ Q,
hdf-ap: X(a),
pi2: snd(t)
Latex:
\mforall{}[A,B:Type]. \mforall{}[Q:bag(B) {}\mrightarrow{} \mBbbP{}].
(Q[\{\}]
{}\mRightarrow{} (\mforall{}b:bag(B). SqStable(Q[b]))
{}\mRightarrow{} (\mforall{}X:\{X:hdataflow(A;B)| hdf-invariant(A;b.Q[b];X)\} . \mforall{}a:A. Q[snd(X(a))]))
Date html generated:
2016_05_16-AM-10_38_50
Last ObjectModification:
2016_01_17-AM-11_12_52
Theory : halting!dataflow
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