Nuprl Lemma : es-knows-stable
∀[poss:EO ─→ ℙ']. ∀[R:PossibleEvent(poss) ─→ PossibleEvent(poss) ─→ ℙ'].
(Trans(PossibleEvent(poss))(R _1 _2)
⇒ (∀e1,e2:PossibleEvent(poss). (e1 ≤ e2 ⇒ (R e1 e2)))
⇒ (∀[P:PossibleEvent(poss) ─→ ℙ']. ∀e1,e2:PossibleEvent(poss). (e1 ≤ e2 ⇒ K(P)@e1 ⇒ K(P)@e2)))
Proof
Definitions occuring in Statement :
poss-le: e1 ≤ e2,
es-knows: K(P)@e,
possible-event: PossibleEvent(poss),
event_ordering: EO,
trans: Trans(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ─→ B[x]
Lemmas :
possible-event_wf,
all_wf,
poss-le_wf,
trans_wf,
event_ordering_wf
\mforall{}[poss:EO {}\mrightarrow{} \mBbbP{}']. \mforall{}[R:PossibleEvent(poss) {}\mrightarrow{} PossibleEvent(poss) {}\mrightarrow{} \mBbbP{}'].
(Trans(PossibleEvent(poss))(R $_{1}$ $_{2}$)
{}\mRightarrow{} (\mforall{}e1,e2:PossibleEvent(poss). (e1 \mleq{} e2 {}\mRightarrow{} (R e1 e2)))
{}\mRightarrow{} (\mforall{}[P:PossibleEvent(poss) {}\mrightarrow{} \mBbbP{}']. \mforall{}e1,e2:PossibleEvent(poss). (e1 \mleq{} e2 {}\mRightarrow{} K(P)@e1 {}\mRightarrow{} K(P)@e2)))
Date html generated:
2015_07_17-AM-08_52_27
Last ObjectModification:
2015_01_27-PM-01_16_10
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