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]
Definitions unfolded in proof :
es-knows: K(P)@e,
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x],
uimplies: b supposing a,
not: ¬A,
false: False,
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
guard: {T},
sym: Sym(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y])
Latex:
\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:
2016_05_16-AM-09_52_49
Last ObjectModification:
2015_12_28-PM-09_34_45
Theory : new!event-ordering
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