Nuprl Lemma : ses-cipher-unique
∀[s:SES]
∀[es:EO+(Info)]. ∀[a,b:E(Encrypt)].
Encrypt(a) = Encrypt(b) ∈ (SecurityData × Key × Atom1) supposing cipherText(a) = cipherText(b) ∈ Atom1
supposing PropertyO
Proof
Definitions occuring in Statement :
ses-ordering: PropertyO,
ses-crypt: cipherText(e),
ses-encrypt: Encrypt,
ses-info: Info,
security-event-structure: SES,
encryption-key: Key,
sdata: SecurityData,
es-E-interface: E(X),
eclass-val: X(e),
event-ordering+: EO+(Info),
atom: Atom$n,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
product: x:A × B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
nat: ℕ,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
and: P ∧ Q,
guard: {T},
es-E-interface: E(X),
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
ses-ordering: PropertyO,
event-has: (e has a),
class-value-has: X(e) has a,
cand: A c∧ B,
sq_type: SQType(T),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
ses-crypt: cipherText(e),
ses-encryption-key: key(e),
ses-encrypted: plainText(e),
pi1: fst(t),
pi2: snd(t),
uiff: uiff(P;Q),
es-causle: e c≤ e',
so_lambda: λ2x.t[x],
so_apply: x[s],
encryption-key: Key,
Id: Id
Latex:
\mforall{}[s:SES]
\mforall{}[es:EO+(Info)]. \mforall{}[a,b:E(Encrypt)].
Encrypt(a) = Encrypt(b) supposing cipherText(a) = cipherText(b)
supposing PropertyO
Date html generated:
2016_05_17-PM-00_24_07
Last ObjectModification:
2016_01_18-AM-07_45_45
Theory : event-logic-applications
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