Nuprl Lemma : es-knows-true
∀[poss:EO ─→ ℙ']. ∀[R:PossibleEvent(poss) ─→ PossibleEvent(poss) ─→ ℙ'].
((∀e:PossibleEvent(poss). (R e e)) ⇒ (∀[P:PossibleEvent(poss) ─→ ℙ']. ∀e:PossibleEvent(poss). (K(P)@e ⇒ (P e))))
Proof
Definitions occuring in Statement :
es-knows: K(P)@e,
possible-event: PossibleEvent(poss),
event_ordering: EO,
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ─→ B[x]
Lemmas :
all_wf,
possible-event_wf,
event_ordering_wf
\mforall{}[poss:EO {}\mrightarrow{} \mBbbP{}']. \mforall{}[R:PossibleEvent(poss) {}\mrightarrow{} PossibleEvent(poss) {}\mrightarrow{} \mBbbP{}'].
((\mforall{}e:PossibleEvent(poss). (R e e))
{}\mRightarrow{} (\mforall{}[P:PossibleEvent(poss) {}\mrightarrow{} \mBbbP{}']. \mforall{}e:PossibleEvent(poss). (K(P)@e {}\mRightarrow{} (P e))))
Date html generated:
2015_07_17-AM-08_52_01
Last ObjectModification:
2015_01_27-PM-01_17_42
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