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]
Definitions unfolded in proof :
es-knows: K(P)@e,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
guard: {T},
trans: Trans(T;x,y.E[x; y])
Latex:
\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:
2016_05_16-AM-09_53_26
Last ObjectModification:
2015_12_28-PM-09_33_07
Theory : new!event-ordering
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