Nuprl Lemma : es-knows-trans
∀[poss:EO ─→ ℙ']. ∀[R:PossibleEvent(poss) ─→ PossibleEvent(poss) ─→ ℙ']. ∀[P,Q:PossibleEvent(poss) ─→ ℙ'].
((∀e:PossibleEvent(poss). ((P e) ⇒ (Q e))) ⇒ (∀e:PossibleEvent(poss). (K(P)@e ⇒ K(Q)@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 :
possible-event_wf,
all_wf,
event_ordering_wf
\mforall{}[poss:EO {}\mrightarrow{} \mBbbP{}']. \mforall{}[R:PossibleEvent(poss) {}\mrightarrow{} PossibleEvent(poss) {}\mrightarrow{} \mBbbP{}'].
\mforall{}[P,Q:PossibleEvent(poss) {}\mrightarrow{} \mBbbP{}'].
((\mforall{}e:PossibleEvent(poss). ((P e) {}\mRightarrow{} (Q e))) {}\mRightarrow{} (\mforall{}e:PossibleEvent(poss). (K(P)@e {}\mRightarrow{} K(Q)@e)))
Date html generated:
2015_07_17-AM-08_52_13
Last ObjectModification:
2015_01_27-PM-01_16_29
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