Nuprl Lemma : causal-class-relation_wf
∀[Info,A:Type]. ∀[R:A ⟶ Info ⟶ ℙ]. ∀[X:EClass(A)]. ∀[es:EO+(Info)].
(for every a in X there is an
earlier event with info=b such that
R[a;b] ∈ ℙ)
Proof
Definitions occuring in Statement :
causal-class-relation: causal-class-relation,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
causal-class-relation: causal-class-relation,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
and: P ∧ Q,
so_apply: x[s1;s2],
so_apply: x[s],
exists: ∃x:A. B[x],
so_lambda: λ2x y.t[x; y]
Latex:
\mforall{}[Info,A:Type]. \mforall{}[R:A {}\mrightarrow{} Info {}\mrightarrow{} \mBbbP{}]. \mforall{}[X:EClass(A)]. \mforall{}[es:EO+(Info)].
(for every a in X there is an
earlier event with info=b such that
R[a;b] \mmember{} \mBbbP{})
Date html generated:
2016_05_16-PM-01_37_48
Last ObjectModification:
2015_12_29-PM-02_07_45
Theory : event-ordering
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