Nuprl Lemma : event-has*-iff
∀s:SES. ∀es:EO+(Info). ∀e:E. ∀a:Atom1. (e has* a ⇐⇒ (e has a) ∨ (∃z:E. ((z ->> e) ∧ z has* a)))
Proof
Definitions occuring in Statement :
event-has*: e has* a,
ses-info-flow: ->>,
event-has: (e has a),
ses-info: Info,
security-event-structure: SES,
event-ordering+: EO+(Info),
es-E: E,
atom: Atom$n,
infix_ap: x f y,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
and: P ∧ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
rev_implies: P ⇐ Q,
or: P ∨ Q,
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
infix_ap: x f y,
so_apply: x[s],
event-has*: e has* a,
rel_star: R^*,
guard: {T},
cand: A c∧ B,
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top
Latex:
\mforall{}s:SES. \mforall{}es:EO+(Info). \mforall{}e:E. \mforall{}a:Atom1. (e has* a \mLeftarrow{}{}\mRightarrow{} (e has a) \mvee{} (\mexists{}z:E. ((z ->> e) \mwedge{} z has* a)))
Date html generated:
2016_05_17-AM-11_48_06
Last ObjectModification:
2016_01_18-AM-07_45_15
Theory : event-logic-applications
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