Nuprl Lemma : ses-is-protocol-action-useable
∀[s:SES]
∀[pa:ProtocolAction]. ∀[es:EO+(Info)]. ∀[e:E]. UseableAtoms(e) = pa-useable(pa) ∈ (Atom1 List) supposing pa(e)
supposing ActionsDisjoint
Proof
Definitions occuring in Statement :
ses-is-protocol-action: pa(e),
pa-useable: pa-useable(pa),
protocol-action: ProtocolAction,
ses-useable-atoms: UseableAtoms(e),
ses-disjoint: ActionsDisjoint,
ses-info: Info,
security-event-structure: SES,
event-ordering+: EO+(Info),
es-E: E,
list: T List,
atom: Atom$n,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
ses-is-protocol-action: pa(e),
protocol-action: ProtocolAction,
pa-useable: pa-useable(pa),
ses-useable-atoms: UseableAtoms(e),
ses-disjoint: ActionsDisjoint,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
decidable: Dec(P),
or: P ∨ Q,
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
prop: ℙ,
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
ses-sig: signature(e),
so_apply: x[s],
so_lambda: λ2x.t[x],
ses-crypt: cipherText(e),
es-E-interface: E(X),
ses-decrypted: plainText(e)
Latex:
\mforall{}[s:SES]
\mforall{}[pa:ProtocolAction]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. UseableAtoms(e) = pa-useable(pa) supposing pa(e)
supposing ActionsDisjoint
Date html generated:
2016_05_17-PM-00_40_17
Last ObjectModification:
2016_01_18-AM-07_46_53
Theory : event-logic-applications
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