Step
*
of 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))]))
BY
{ (Auto THEN D -2 THEN Unhide THEN Auto) }
1
1. A : Type
2. B : Type
3. Q : bag(B) ─→ ℙ
4. Q[{}]@i
5. ∀b:bag(B). SqStable(Q[b])@i
6. X : hdataflow(A;B)@i
7. hdf-invariant(A;b.Q[b];X)@i
8. a : A@i
⊢ Q[snd(X(a))]
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))]))
By
(Auto THEN D -2 THEN Unhide THEN Auto)
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