Nuprl Lemma : causal-invariant_wf
∀[Info:Type]. ∀[R:Id ⟶ Id ⟶ Info List+ ⟶ Info List+ ⟶ ℙ]. ∀[P:Id ⟶ Info List+ ⟶ ℙ].
(causal-invariant(i,L.P[i;L];a,b,L1,L2.R[a;b;L1;L2]) ∈ EO+(Info) ⟶ ℙ)
Proof
Definitions occuring in Statement :
causal-invariant: causal-invariant(i,L.P[i; L];a,b,L1,L2.R[a; b; L1; L2]),
event-ordering+: EO+(Info),
Id: Id,
listp: A List+,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2;s3;s4],
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-invariant: causal-invariant(i,L.P[i; L];a,b,L1,L2.R[a; b; L1; L2]),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
and: P ∧ Q,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_apply: x[s],
exists: ∃x:A. B[x]
Latex:
\mforall{}[Info:Type]. \mforall{}[R:Id {}\mrightarrow{} Id {}\mrightarrow{} Info List\msupplus{} {}\mrightarrow{} Info List\msupplus{} {}\mrightarrow{} \mBbbP{}]. \mforall{}[P:Id {}\mrightarrow{} Info List\msupplus{} {}\mrightarrow{} \mBbbP{}].
(causal-invariant(i,L.P[i;L];a,b,L1,L2.R[a;b;L1;L2]) \mmember{} EO+(Info) {}\mrightarrow{} \mBbbP{})
Date html generated:
2016_05_16-PM-01_24_38
Last ObjectModification:
2015_12_29-PM-02_01_28
Theory : event-ordering
Home
Index