Nuprl Lemma : flow-graph-information-flow-relation

∀[Info,T:Type].
  ∀S:Id List. ∀G:Graph(S). ∀F:information-flow(T;S). ∀es:EO+(Info). ∀X:EClass(T). ∀e:E(X). ∀i:Id.
    ((i ∈ S)
    ⇒ es-interface-locs-list(es;X;S)
    ⇒ flow-graph(S;T;F;G)
    ⇒ (loc(e)⟶i)∈G supposing information-flow-relation(es;X;F;e;i))

Proof

Definitions occuring in Statement : information-flow-relation: information-flow-relation(es;X;F;e;i), es-interface-locs-list: es-interface-locs-list(es;X;S), es-E-interface: E(X), eclass: EClass(A[eo; e]), event-ordering+: EO+(Info), flow-graph: flow-graph(S;T;F;G), information-flow: information-flow(T;S), es-loc: loc(e), id-graph-edge: (i⟶j)∈G, id-graph: Graph(S), Id: Id, l_member: (x ∈ l), list: T List, uimplies: b supposing a, uall: ∀[x:A]. B[x], all: ∀x:A. B[x], implies: P ⇒ Q, universe: Type
Definitions unfolded in proof : uall: ∀[x:A]. B[x], all: ∀x:A. B[x], implies: P ⇒ Q, uimplies: b supposing a, member: t ∈ T, information-flow-relation: information-flow-relation(es;X;F;e;i), prop: ℙ, subtype_rel: A ⊆r B, so_lambda: λ₂x y.t[x; y], so_apply: x[s1;s2], top: Top, information-flow: information-flow(T;S), es-E-interface: E(X), can-apply: can-apply(f;x), guard: {T}, es-interface-locs-list: es-interface-locs-list(es;X;S), flow-graph: flow-graph(S;T;F;G)

Latex:
\mforall{}[Info,T:Type]. \mforall{}S:Id List. \mforall{}G:Graph(S). \mforall{}F:information-flow(T;S). \mforall{}es:EO+(Info). \mforall{}X:EClass(T). \mforall{}e:E(X). \mforall{}i:Id. ((i \mmember{} S) {}\mRightarrow{} es-interface-locs-list(es;X;S) {}\mRightarrow{} flow-graph(S;T;F;G) {}\mRightarrow{} (loc(e){}\mrightarrow{}i)\mmember{}G supposing information-flow-relation(es;X;F;e;i)) Date html generated: 2016_05_16-PM-11_13_55 Last ObjectModification: 2015_12_29-AM-10_37_41 Theory : event-ordering Home Index