Nuprl Lemma : correct-causal-class-relation_wf
∀[Correct:Id ⟶ ℙ]. ∀[Info,A:Type]. ∀[R:A ⟶ Info ⟶ ℙ]. ∀[X:EClass(A)]. ∀[es:EO+(Info)].
(for every a in X at location i s.t. Correct[i] there is an earlier event with info=b such that R[a;b] ∈ ℙ)
Proof
Definitions occuring in Statement :
correct-causal-class-relation: for every a in X at location i s.t. Correct[i] there is an earlier event with info=b such that R[a; b],
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
correct-causal-class-relation: for every a in X at location i s.t. Correct[i] there is an earlier event with info=b such that R[a; b],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
and: P ∧ Q,
so_apply: x[s1;s2],
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
so_lambda: λ2x y.t[x; y]
Latex:
\mforall{}[Correct:Id {}\mrightarrow{} \mBbbP{}]. \mforall{}[Info,A:Type]. \mforall{}[R:A {}\mrightarrow{} Info {}\mrightarrow{} \mBbbP{}]. \mforall{}[X:EClass(A)]. \mforall{}[es:EO+(Info)].
(for every a in X at location i s.t. Correct[i] there is an earlier event with info=b
such that R[a;b] \mmember{} \mBbbP{})
Date html generated:
2016_05_16-PM-01_38_07
Last ObjectModification:
2015_12_29-PM-02_08_06
Theory : event-ordering
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