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)
Lemmas :
hdf-ap_wf,
set_wf,
hdataflow_wf,
hdf-invariant_wf,
bag_wf,
all_wf,
sq_stable_wf,
empty-bag_wf,
nil_wf,
iter_hdf_nil_lemma,
hdataflow-ext,
unit_wf2,
true_wf
\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:
2015_07_17-AM-08_05_13
Last ObjectModification:
2015_01_27-PM-00_16_26
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