Nuprl Lemma : es-knows-not
∀[poss:EO ─→ ℙ']. ∀[R:PossibleEvent(poss) ─→ PossibleEvent(poss) ─→ ℙ'].
(EquivRel(PossibleEvent(poss))(R _1 _2)
⇒ (∀[P:PossibleEvent(poss) ─→ ℙ']. ∀e:PossibleEvent(poss). K(λe.(¬K(P)@e))@e supposing ¬K(P)@e))
Proof
Definitions occuring in Statement :
es-knows: K(P)@e,
possible-event: PossibleEvent(poss),
event_ordering: EO,
equiv_rel: EquivRel(T;x,y.E[x; y]),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
apply: f a,
lambda: λx.A[x],
function: x:A ─→ B[x]
Lemmas :
all_wf,
possible-event_wf,
not_wf,
equiv_rel_wf,
event_ordering_wf
\mforall{}[poss:EO {}\mrightarrow{} \mBbbP{}']. \mforall{}[R:PossibleEvent(poss) {}\mrightarrow{} PossibleEvent(poss) {}\mrightarrow{} \mBbbP{}'].
(EquivRel(PossibleEvent(poss))(R $_{1}$ $_{2}$)
{}\mRightarrow{} (\mforall{}[P:PossibleEvent(poss) {}\mrightarrow{} \mBbbP{}']. \mforall{}e:PossibleEvent(poss). K(\mlambda{}e.(\mneg{}K(P)@e))@e supposing \mneg{}K(P)@e))
Date html generated:
2015_07_17-AM-08_52_09
Last ObjectModification:
2015_01_27-PM-01_17_46
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